{"id":8926,"date":"2017-04-27T21:20:23","date_gmt":"2017-04-27T21:20:23","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&p=8926"},"modified":"2024-05-02T16:53:25","modified_gmt":"2024-05-02T16:53:25","slug":"problem-set","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/problem-set\/","title":{"raw":"Problem Set: Graphs","rendered":"Problem Set: Graphs"},"content":{"raw":"

Practice Makes Perfect<\/h2>\r\nPlot Points on a Rectangular Coordinate System<\/strong>\r\nIn the following exercises, plot each point on a coordinate grid.\r\n\r\n[latex]\\left(3,2\\right)[\/latex]\r\n\r\n\"The\r\n\r\n[latex]\\left(4,1\\right)[\/latex]\r\n\r\n[latex]\\left(1,5\\right)[\/latex]\r\n\r\n\"The\r\n\r\n[latex]\\left(3,4\\right)[\/latex]\r\n\r\n[latex]\\left(4,1\\right),\\left(1,4\\right)[\/latex]\r\n\r\n\"The\r\n\r\n[latex]\\left(3,2\\right),\\left(2,3\\right)[\/latex]\r\n\r\n[latex]\\left(3,4\\right),\\left(4,3\\right)[\/latex]\r\n\r\n\"The\r\n\r\nIn the following exercises, plot each point on a coordinate grid and identify the quadrant in which the point is located.\r\n\r\n\u24d0 [latex]\\left(-4,2\\right)[\/latex]\r\n\u24d1 [latex]\\left(-1,-2\\right)[\/latex]\r\n\u24d2 [latex]\\left(3,-5\\right)[\/latex]\r\n\u24d3 [latex]\\left(2,\\Large\\frac{5}{2}\\normalsize\\right)[\/latex]\r\n\r\n\u24d0 [latex]\\left(-2,-3\\right)[\/latex]\r\n\u24d1 [latex]\\left(3,-3\\right)[\/latex]\r\n\u24d2 [latex]\\left(-4,1\\right)[\/latex]\r\n\u24d3 [latex]\\left(1,\\Large\\frac{3}{2}\\normalsize\\right)[\/latex]\r\n\r\n\"The\r\n\r\n\u24d0 [latex]\\left(-1,1\\right)[\/latex]\r\n\u24d1 [latex]\\left(-2,-1\\right)[\/latex]\r\n\u24d2 [latex]\\left(1,-4\\right)[\/latex]\r\n\u24d3 [latex]\\left(3,\\Large\\frac{7}{2}\\normalsize\\right)[\/latex]\r\n\r\n\u24d0 [latex]\\left(3,-2\\right)[\/latex]\r\n\u24d1 [latex]\\left(-3,2\\right)[\/latex]\r\n\u24d2 [latex]\\left(-3,-2\\right)[\/latex]\r\n\u24d3 [latex]\\left(3,2\\right)[\/latex]\r\n\r\n\"The\r\n\r\n\u24d0 [latex]\\left(4,-1\\right)[\/latex]\r\n\u24d1 [latex]\\left(-4,1\\right)[\/latex]\r\n\u24d2 [latex]\\left(-4,-1\\right)[\/latex]\r\n\u24d3 [latex]\\left(4,1\\right)[\/latex]\r\n\r\n\u24d0 [latex]\\left(-2,0\\right)[\/latex]\r\n\u24d1 [latex]\\left(-3,0\\right)[\/latex]\r\n\u24d2 [latex]\\left(0,4\\right)[\/latex]\r\n\u24d3 [latex]\\left(0,2\\right)[\/latex]\r\n\r\n\"The\r\n\r\nIdentify Points on a Graph<\/strong>\r\nIn the following exercises, name the ordered pair of each point shown.\r\n\r\n\"The\r\n\r\n\"TThe\r\n\r\n\"The\r\n\r\n\"The\r\n\r\n\"The\r\n\r\n\"The\r\n\r\n\"The\r\n\r\nVerify Solutions to an Equation in Two Variables<\/strong>\r\nIn the following exercises, determine which ordered pairs are solutions to the given equation.\r\n\r\n[latex]2x+y=6[\/latex]\r\n\r\n\u24d0 [latex]\\left(1,4\\right)[\/latex]\r\n\u24d1 [latex]\\left(3,0\\right)[\/latex]\r\n\u24d2 [latex]\\left(2,3\\right)[\/latex]\r\n\r\n\u24d0, \u24d1\r\n\r\n[latex]x+3y=9[\/latex]\r\n
    \r\n \t
  1. \u24d0 [latex]\\left(0,3\\right)[\/latex]<\/li>\r\n \t
  2. \u24d1 [latex]\\left(6,1\\right)[\/latex]<\/li>\r\n \t
  3. \u24d2 [latex]\\left(-3,-3\\right)[\/latex]<\/li>\r\n<\/ol>\r\n[latex]4x - 2y=8[\/latex]\r\n\r\n\u24d0 [latex]\\left(3,2\\right)[\/latex]\r\n\u24d1 [latex]\\left(1,4\\right)[\/latex]\r\n\u24d2 [latex]\\left(0,-4\\right)[\/latex]\r\n\r\n\u24d0, \u24d2\r\n\r\n[latex]3x - 2y=12[\/latex]\r\n\r\n\u24d0 [latex]\\left(4,0\\right)[\/latex]\r\n\u24d1 [latex]\\left(2,-3\\right)[\/latex]\r\n\u24d2 [latex]\\left(1,6\\right)[\/latex]\r\n\r\n[latex]y=4x+3[\/latex]\r\n\r\n\u24d0 [latex]\\left(4,3\\right)[\/latex]\r\n\u24d1 [latex]\\left(-1,-1\\right)[\/latex]\r\n\u24d2 [latex]\\left(\\Large\\frac{1}{2}\\normalsize,5\\right)[\/latex]\r\n\r\n\u24d1, \u24d2\r\n\r\n[latex]y=2x - 5[\/latex]\r\n\r\n\u24d0 [latex]\\left(0,-5\\right)[\/latex]\r\n\u24d1 [latex]\\left(2,1\\right)[\/latex]\r\n\u24d2 [latex]\\left(\\Large\\frac{1}{2}\\normalsize ,-4\\right)[\/latex]\r\n\r\n[latex]y=\\Large\\frac{1}{2}\\normalsize x - 1[\/latex]\r\n\r\n\u24d0 [latex]\\left(2,0\\right)[\/latex]\r\n\u24d1 [latex]\\left(-6,-4\\right)[\/latex]\r\n\u24d2 [latex]\\left(-4,-1\\right)[\/latex]\r\n\r\n\u24d0, \u24d1\r\n\r\n[latex]y=\\Large\\frac{1}{3}\\normalsize x+1[\/latex]\r\n\r\n\u24d0 [latex]\\left(-3,0\\right)[\/latex]\r\n\u24d1 [latex]\\left(9,4\\right)[\/latex]\r\n\u24d2 [latex]\\left(-6,-1\\right)[\/latex]\r\n\r\nFind Solutions to Linear Equations in Two Variables<\/strong>\r\nIn the following exercises, complete the table to find solutions to each linear equation.\r\n\r\n[latex]y=2x - 4[\/latex]\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    [latex]x[\/latex]<\/th>\r\n[latex]y[\/latex]<\/th>\r\n[latex]\\left(x,y\\right)[\/latex]<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
    [latex]-1[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
    [latex]0[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
    [latex]2[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    [latex]x[\/latex]<\/th>\r\n[latex]y[\/latex]<\/th>\r\n[latex]\\left(x,y\\right)[\/latex]<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
    [latex]-1[\/latex]<\/td>\r\n[latex]-6[\/latex]<\/td>\r\n[latex]\\left(-1,-6\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
    [latex]0[\/latex]<\/td>\r\n[latex]-4[\/latex]<\/td>\r\n[latex]\\left(0,-4\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
    [latex]2[\/latex]<\/td>\r\n[latex]0[\/latex]<\/td>\r\n[latex]\\left(2,0\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[latex]y=3x - 1[\/latex]\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    [latex]x[\/latex]<\/th>\r\n[latex]y[\/latex]<\/th>\r\n[latex]\\left(x,y\\right)[\/latex]<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
    [latex]-1[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
    [latex]0[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
    [latex]2[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[latex]y=-x+5[\/latex]\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    [latex]x[\/latex]<\/th>\r\n[latex]y[\/latex]<\/th>\r\n[latex]\\left(x,y\\right)[\/latex]<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
    [latex]-2[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
    [latex]0[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
    [latex]3[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    [latex]x[\/latex]<\/th>\r\n[latex]y[\/latex]<\/th>\r\n[latex]\\left(x,y\\right)[\/latex]<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
    [latex]-2[\/latex]<\/td>\r\n[latex]7[\/latex]<\/td>\r\n[latex]\\left(-2,7\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
    [latex]0[\/latex]<\/td>\r\n[latex]5[\/latex]<\/td>\r\n[latex]\\left(0,5\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
    [latex]3[\/latex]<\/td>\r\n[latex]2[\/latex]<\/td>\r\n[latex]\\left(3,2\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[latex]y=\\Large\\frac{1}{3}\\normalsize x+1[\/latex]\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    [latex]x[\/latex]<\/th>\r\n[latex]y[\/latex]<\/th>\r\n[latex]\\left(x,y\\right)[\/latex]<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
    [latex]0[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
    [latex]3[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
    [latex]6[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[latex]y=-\\Large\\frac{3}{2}\\normalsize x - 2[\/latex]\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    [latex]x[\/latex]<\/th>\r\n[latex]y[\/latex]<\/th>\r\n[latex]\\left(x,y\\right)[\/latex]<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
    [latex]-2[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
    [latex]0[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
    [latex]2[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    [latex]x[\/latex]<\/th>\r\n[latex]y[\/latex]<\/th>\r\n[latex]\\left(x,y\\right)[\/latex]<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
    [latex]-2[\/latex]<\/td>\r\n[latex]1[\/latex]<\/td>\r\n[latex]\\left(-2,1\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
    [latex]0[\/latex]<\/td>\r\n[latex]-2[\/latex]<\/td>\r\n[latex]\\left(0,-2\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
    [latex]2[\/latex]<\/td>\r\n[latex]-5[\/latex]<\/td>\r\n[latex]\\left(2,-5\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[latex]x+2y=8[\/latex]\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    [latex]x[\/latex]<\/th>\r\n[latex]y[\/latex]<\/th>\r\n[latex]\\left(x,y\\right)[\/latex]<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
    [latex]0[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
    [latex]4[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
    <\/td>\r\n[latex]0[\/latex]<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

    Everyday Math<\/h2>\r\nWeight of a baby<\/strong> Mackenzie recorded her baby\u2019s weight every two months. The baby\u2019s age, in months, and weight, in pounds, are listed in the table, and shown as an ordered pair in the third column.\r\n\u24d0 Plot the points on a coordinate grid.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    [latex]\\text{Age}[\/latex]<\/td>\r\n[latex]\\text{Weight}[\/latex]<\/td>\r\n[latex]\\left(x,y\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
    [latex]0[\/latex]<\/td>\r\n[latex]7[\/latex]<\/td>\r\n[latex]\\left(0,7\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
    [latex]2[\/latex]<\/td>\r\n[latex]11[\/latex]<\/td>\r\n[latex]\\left(2,11\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
    [latex]4[\/latex]<\/td>\r\n[latex]15[\/latex]<\/td>\r\n[latex]\\left(4,15\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
    [latex]6[\/latex]<\/td>\r\n[latex]16[\/latex]<\/td>\r\n[latex]\\left(6,16\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
    [latex]8[\/latex]<\/td>\r\n[latex]19[\/latex]<\/td>\r\n[latex]\\left(8,19\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
    [latex]10[\/latex]<\/td>\r\n[latex]20[\/latex]<\/td>\r\n[latex]\\left(10,20\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
    [latex]12[\/latex]<\/td>\r\n[latex]21[\/latex]<\/td>\r\n[latex]\\left(12,21\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\u24d1 Why is only Quadrant I needed?\r\n\r\n\u24d0\r\n\r\n\"This\r\n\u24d1 Age and weight are only positive.\r\n\r\nWeight of a child<\/strong> Latresha recorded her son\u2019s height and weight every year. His height, in inches, and weight, in pounds, are listed in the table, and shown as an ordered pair in the third column.\r\n\u24d0 Plot the points on a coordinate grid.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    [latex]\\begin{array}{c}\\text{Height}\\hfill \\\\ x\\hfill \\end{array}[\/latex]<\/td>\r\n[latex]\\begin{array}{c}\\text{Weight}\\hfill \\\\ y\\hfill \\end{array}[\/latex]<\/td>\r\n[latex]\\begin{array}{}\\\\ \\left(x,y\\right)\\hfill \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n
    [latex]28[\/latex]<\/td>\r\n[latex]22[\/latex]<\/td>\r\n[latex]\\left(28,22\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
    [latex]31[\/latex]<\/td>\r\n[latex]27[\/latex]<\/td>\r\n[latex]\\left(31,27\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
    [latex]33[\/latex]<\/td>\r\n[latex]33[\/latex]<\/td>\r\n[latex]\\left(33,33\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
    [latex]37[\/latex]<\/td>\r\n[latex]35[\/latex]<\/td>\r\n[latex]\\left(37,35\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
    [latex]40[\/latex]<\/td>\r\n[latex]41[\/latex]<\/td>\r\n[latex]\\left(40,41\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
    [latex]42[\/latex]<\/td>\r\n[latex]45[\/latex]<\/td>\r\n[latex]\\left(42,45\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\u24d1 Why is only Quadrant I needed?\r\n

    Writing Exercises<\/h2>\r\nHave you ever used a map with a rectangular coordinate system? Describe the map and how you used it.\r\n\r\nAnswers may vary.\r\n\r\nHow do you determine if an ordered pair is a solution to a given equation?\r\n

    Self Check<\/h2>\r\n\u24d0 After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.\r\n\r\n\"Checklist\r\n\u24d1 If most of your checks were:\r\n\u2026confidently. Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific.\r\n\u2026with some help. This must be addressed quickly because topics you do not master become potholes in your road to success. In math, every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Who can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?\r\n\u2026no\u2014I don\u2019t get it! This is a warning sign and you must not ignore it. You should get help right away or you will quickly be overwhelmed. See your instructor as soon as you can to discuss your situation. Together\r\n\r\n \r\n\r\n \r\n

    Practice Makes Perfect<\/h2>\r\nIdentify the Intercepts on a Graph<\/strong>\r\nIn the following exercises, find the [latex]x\\text{-}[\/latex] and [latex]y\\text{-}[\/latex] intercepts.\r\n\r\n\"The\r\n\r\n(3,0),(0,3)\r\n\r\n\"The\r\n\r\n\"The\r\n\r\n(5,0),(0,\u22125)\r\n\r\n\"The\r\n\r\n\"The\r\n\r\n(\u22122,0),(0,\u22122)\r\n\r\n\"The\r\n\r\n\"The\r\n\r\n(\u22121,0),(0,1)\r\n\r\n\"The\r\n\r\n\"The\r\n\r\n(0,0)\r\n\r\n\"The\r\n\r\nFind the [latex]x[\/latex] and [latex]y[\/latex] Intercepts from an Equation of a Line<\/strong>\r\nIn the following exercises, find the intercepts.\r\n\r\n[latex]x+y=4[\/latex]\r\n\r\n(4,0),(0,4)\r\n\r\n[latex]x+y=3[\/latex]\r\n\r\n[latex]x+y=-2[\/latex]\r\n\r\n(\u22122,0),(0,\u22122)\r\n\r\n[latex]x+y=-5[\/latex]\r\n\r\n[latex]x-y=5[\/latex]\r\n\r\n(5,0),(0,\u22125)\r\n\r\n[latex]x-y=1[\/latex]\r\n\r\n[latex]x-y=-3[\/latex]\r\n\r\n(\u22123,0),(0,3)\r\n\r\n[latex]x-y=-4[\/latex]\r\n\r\n[latex]x+2y=8[\/latex]\r\n\r\n(8,0),(0,4)\r\n\r\n[latex]x+2y=10[\/latex]\r\n\r\n[latex]3x+y=6[\/latex]\r\n\r\n(2,0),(0,6)\r\n\r\n[latex]3x+y=9[\/latex]\r\n\r\n[latex]x - 3y=12[\/latex]\r\n\r\n(12,0),(0,\u22124)\r\n\r\n[latex]x - 2y=8[\/latex]\r\n\r\n[latex]4x-y=8[\/latex]\r\n\r\n(2,0),(0,\u22128)\r\n\r\n[latex]5x-y=5[\/latex]\r\n\r\n[latex]2x+5y=10[\/latex]\r\n\r\n(5,0),(0,2)\r\n\r\n[latex]2x+3y=6[\/latex]\r\n\r\n[latex]3x - 2y=12[\/latex]\r\n\r\n(4,0),(0,\u22126)\r\n\r\n[latex]3x - 5y=30[\/latex]\r\n\r\n[latex]y=\\Large\\frac{1}{3}\\normalsize x - 1[\/latex]\r\n\r\n(3,0),(0,\u22121)\r\n\r\n[latex]y=\\Large\\frac{1}{4}\\normalsize x - 1[\/latex]\r\n\r\n[latex]y=\\Large\\frac{1}{5}\\normalsize x+2[\/latex]\r\n\r\n(\u221210,0),(0,2)\r\n\r\n[latex]y=\\Large\\frac{1}{3}\\normalsize x+4[\/latex]\r\n\r\n[latex]y=3x[\/latex]\r\n\r\n(0,0)\r\n\r\n[latex]y=-2x[\/latex]\r\n\r\n[latex]y=-4x[\/latex]\r\n\r\n(0,0)\r\n\r\n[latex]y=5x[\/latex]\r\n\r\nGraph a Line Using the Intercepts<\/strong>\r\nIn the following exercises, graph using the intercepts.\r\n\r\n[latex]-x+5y=10[\/latex]\r\n\r\n\"The\r\n\r\n[latex]-x+4y=8[\/latex]\r\n\r\n[latex]x+2y=4[\/latex]\r\n\r\n\"The\r\n\r\n[latex]x+2y=6[\/latex]\r\n\r\n[latex]x+y=2[\/latex]\r\n\r\n\"The\r\n\r\n[latex]x+y=5[\/latex]\r\n\r\n[latex]x+y=-3[\/latex]\r\n\r\n\"The\r\n\r\n[latex]x+y=-1[\/latex]\r\n\r\n[latex]x-y=1[\/latex]\r\n\r\n\"The\r\n\r\n[latex]x-y=2[\/latex]\r\n\r\n[latex]x-y=-4[\/latex]\r\n\r\n\"The\r\n\r\n[latex]x-y=-3[\/latex]\r\n\r\n[latex]4x+y=4[\/latex]\r\n\r\n\"The\r\n\r\n[latex]3x+y=3[\/latex]\r\n\r\n[latex]3x-y=-6[\/latex]\r\n\r\n\"The\r\n\r\n[latex]2x-y=-8[\/latex]\r\n\r\n[latex]2x+4y=12[\/latex]\r\n\r\n\"The\r\n\r\n[latex]3x+2y=12[\/latex]\r\n\r\n[latex]3x - 2y=6[\/latex]\r\n\r\n\"The\r\n\r\n[latex]5x - 2y=10[\/latex]\r\n\r\n[latex]2x - 5y=-20[\/latex]\r\n\r\n\"The\r\n\r\n[latex]3x - 4y=-12[\/latex]\r\n\r\n[latex]y=-2x[\/latex]\r\n\r\n\"The\r\n\r\n[latex]y=-4x[\/latex]\r\n\r\n[latex]y=x[\/latex]\r\n\r\n\"The\r\n\r\n[latex]y=3x[\/latex]\r\n\r\nChoose the Most Convenient Method to Graph a Line<\/strong>\r\nIn the following exercises, identify the most convenient method to graph each line.\r\n\r\n[latex]x=2[\/latex]\r\n\r\nvertical line\r\n\r\n[latex]y=4[\/latex]\r\n\r\n[latex]y=5[\/latex]\r\n\r\nhorizontal line\r\n\r\n[latex]x=-3[\/latex]\r\n\r\n[latex]y=-3x+4[\/latex]\r\n\r\nplotting points\r\n\r\n[latex]y=-5x+2[\/latex]\r\n\r\n[latex]x-y=5[\/latex]\r\n\r\nintercepts\r\n\r\n[latex]x-y=1[\/latex]\r\n\r\n[latex]y=\\Large\\frac{2}{3}\\normalsize x - 1[\/latex]\r\n\r\nplotting points\r\n\r\n[latex]y=\\Large\\frac{4}{5}\\normalsize x - 3[\/latex]\r\n\r\n[latex]y=-3[\/latex]\r\n\r\nhorizontal line\r\n\r\n[latex]y=-1[\/latex]\r\n\r\n[latex]3x - 2y=-12[\/latex]\r\n\r\nintercepts\r\n\r\n[latex]2x - 5y=-10[\/latex]\r\n\r\n[latex]y=-\\Large\\frac{1}{4}\\normalsize x+3[\/latex]\r\n\r\nplotting points\r\n\r\n[latex]y=-\\Large\\frac{1}{3}\\normalsize x+5[\/latex]\r\n

    Everyday Math<\/h2>\r\nRoad trip<\/strong> Damien is driving from Chicago to Denver, a distance of [latex]1,000[\/latex] miles. The [latex]x\\text{-axis}[\/latex] on the graph below shows the time in hours since Damien left Chicago. The [latex]y\\text{-axis}[\/latex] represents the distance he has left to drive.\r\n\r\n\"The\r\n\u24d0 Find the [latex]x\\text{-}[\/latex] and [latex]y\\text{-}[\/latex] intercepts\r\n\u24d1 Explain what the [latex]x\\text{-}[\/latex] and [latex]y\\text{-}[\/latex] intercepts mean for Damien.\r\n\r\n\u24d0 (0,1,000),(15,0). \u24d1 At (0,1,000) he left Chicago 0 hours ago and has 1,000 miles left to drive. At (15,0) he left Chicago 15 hours ago and has 0 miles left to drive.\r\n\r\nRoad trip<\/strong> Ozzie filled up the gas tank of his truck and went on a road trip. The [latex]x\\text{-axis}[\/latex] on the graph shows the number of miles Ozzie drove since filling up. The [latex]y\\text{-axis}[\/latex] represents the number of gallons of gas in the truck\u2019s gas tank.\r\n\r\n\"The\r\n\u24d0 Find the [latex]x\\text{-}[\/latex] and [latex]y\\text{-}[\/latex] intercepts.\r\n\u24d1 Explain what the [latex]x\\text{-}[\/latex] and [latex]y\\text{-}[\/latex] intercepts mean for Ozzie.\r\n

    Writing Exercises<\/h2>\r\nHow do you find the [latex]x\\text{-intercept}[\/latex] of the graph of [latex]3x - 2y=6?[\/latex]\r\n\r\nAnswers will vary.\r\n\r\nHow do you find the [latex]y\\text{-intercept}[\/latex] of the graph of [latex]5x-y=10?[\/latex]\r\n\r\nDo you prefer to graph the equation [latex]4x+y=-4[\/latex] by plotting points or intercepts? Why?\r\n\r\nAnswers will vary.\r\n\r\nDo you prefer to graph the equation [latex]y=\\Large\\frac{2}{3}\\normalsize x - 2[\/latex] by plotting points or intercepts? Why?\r\n

    Self Check<\/h2>\r\n\u24d0 After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.\r\n\r\n\"Checklist\r\n\u24d1 What does this checklist tell you about your mastery of this section? What steps will you take to improve?\r\n\r\n \r\n

    Practice Makes Perfect<\/h2>\r\nUse Geoboards to Model Slope - CODE THESE in OHM<\/strong>\r\nIn the following exercises, find the slope modeled on each geoboard.\r\n\r\n\"The\r\n\r\n[latex]\\Large\\frac{1}{4}[\/latex]\r\n\r\n\"The\r\n\r\n\"The\r\n\r\n[latex]-\\Large\\frac{3}{2}[\/latex]\r\n\r\n\"The\r\n\r\nIn the following exercises, model each slope. Draw a picture to show your results.\r\n\r\n[latex]\\Large\\frac{2}{3}[\/latex]\r\n\r\n\"The\r\n\r\n[latex]\\Large\\frac{3}{4}[\/latex]\r\n\r\n[latex]\\Large\\frac{1}{4}[\/latex]\r\n\r\n\"The\r\n\r\n[latex]\\Large\\frac{4}{3}[\/latex]\r\n\r\n[latex]-\\Large\\frac{1}{2}[\/latex]\r\n\r\n\"The\r\n\r\n[latex]-\\Large\\frac{3}{4}[\/latex]\r\n\r\n[latex]-\\Large\\frac{2}{3}[\/latex]\r\n\r\n\"The\r\n\r\n[latex]-\\Large\\frac{3}{2}[\/latex]\r\n\r\nFind the Slope of a Line from its Graph<\/strong>\r\nIn the following exercises, find the slope of each line shown.\r\n\r\n\"The\r\n\r\n[latex]\\Large\\frac{2}{5}[\/latex]\r\n\r\n\"The\r\n\r\n\"The\r\n\r\n[latex]\\Large\\frac{5}{4}[\/latex]\r\n\r\n\"The\r\n\r\n\"The\r\n\r\n[latex]-\\Large\\frac{1}{3}[\/latex]\r\n\r\n\"The\r\n\r\n\"The\r\n\r\n[latex]-\\Large\\frac{3}{4}[\/latex]\r\n\r\n\"The\r\n\r\n\"The\r\n\r\n[latex]\\Large\\frac{3}{4}[\/latex]\r\n\r\n\"The\r\n\r\n\"The\r\n\r\n[latex]-\\Large\\frac{5}{2}[\/latex]\r\n\r\n\"The\r\n\r\n\"The\r\n\r\n[latex]-\\Large\\frac{2}{3}[\/latex]\r\n\r\n\"The\r\n\r\n\"The\r\n\r\n[latex]\\Large\\frac{1}{4}[\/latex]\r\n\r\n\"The\r\n\r\nFind the Slope of Horizontal and Vertical Lines<\/strong>\r\nIn the following exercises, find the slope of each line.\r\n\r\n[latex]y=3[\/latex]\r\n\r\n0\r\n\r\n[latex]y=1[\/latex]\r\n\r\n[latex]x=4[\/latex]\r\n\r\nundefined\r\n\r\n[latex]x=2[\/latex]\r\n\r\n[latex]y=-2[\/latex]\r\n\r\n0\r\n\r\n[latex]y=-3[\/latex]\r\n\r\n[latex]x=-5[\/latex]\r\n\r\nundefined\r\n\r\n[latex]x=-4[\/latex]\r\n\r\nUse the Slope Formula to find the Slope of a Line between Two Points<\/strong>\r\nIn the following exercises, use the slope formula to find the slope of the line between each pair of points.\r\n\r\n[latex]\\left(1,4\\right),\\left(3,9\\right)[\/latex]\r\n\r\n[latex]\\Large\\frac{5}{2}[\/latex]\r\n\r\n[latex]\\left(2,3\\right),\\left(5,7\\right)[\/latex]\r\n\r\n[latex]\\left(0,3\\right),\\left(4,6\\right)[\/latex]\r\n\r\n[latex]\\Large\\frac{3}{4}[\/latex]\r\n\r\n[latex]\\left(0,1\\right),\\left(5,4\\right)[\/latex]\r\n\r\n[latex]\\left(2,5\\right),\\left(4,0\\right)[\/latex]\r\n\r\n[latex]-\\Large\\frac{5}{2}[\/latex]\r\n\r\n[latex]\\left(3,6\\right),\\left(8,0\\right)[\/latex]\r\n\r\n[latex]\\left(-3,3\\right),\\left(2,-5\\right)[\/latex]\r\n\r\n[latex]-\\Large\\frac{8}{5}[\/latex]\r\n\r\n[latex]\\left(-2,4\\right),\\left(3,-1\\right)[\/latex]\r\n\r\n[latex]\\left(-1,-2\\right),\\left(2,5\\right)[\/latex]\r\n\r\n[latex]\\Large\\frac{7}{3}[\/latex]\r\n\r\n[latex]\\left(-2,-1\\right),\\left(6,5\\right)[\/latex]\r\n\r\n[latex]\\left(4,-5\\right),\\left(1,-2\\right)[\/latex]\r\n\r\n\u22121\r\n\r\n[latex]\\left(3,-6\\right),\\left(2,-2\\right)[\/latex]\r\n\r\nGraph a Line Given a Point and the Slope<\/strong>\r\nIn the following exercises, graph the line given a point and the slope.\r\n\r\n[latex]\\left(1,-2\\right);m=\\Large\\frac{3}{4}[\/latex]\r\n\r\n\"The\r\n\r\n[latex]\\left(1,-1\\right);m=\\Large\\frac{1}{2}[\/latex]\r\n\r\n[latex]\\left(2,5\\right);m=-\\Large\\frac{1}{3}[\/latex]\r\n\r\n\"The\r\n\r\n[latex]\\left(1,4\\right);m=-\\Large\\frac{1}{2}[\/latex]\r\n\r\n[latex]\\left(-3,4\\right);m=-\\Large\\frac{3}{2}[\/latex]\r\n\r\n\"The\r\n\r\n[latex]\\left(-2,5\\right);m=-\\Large\\frac{5}{4}[\/latex]\r\n\r\n[latex]\\left(-1,-4\\right);m=\\Large\\frac{4}{3}[\/latex]\r\n\r\n\"The\r\n\r\n[latex]\\left(-3,-5\\right);m=\\Large\\frac{3}{2}[\/latex]\r\n\r\n[latex]\\left(0,3\\right);m=-\\Large\\frac{2}{5}[\/latex]\r\n\r\n\"The\r\n\r\n[latex]\\left(0,5\\right);m=-\\Large\\frac{4}{3}[\/latex]\r\n\r\n[latex]\\left(-2,0\\right);m=\\Large\\frac{3}{4}[\/latex]\r\n\r\n\"The\r\n\r\n[latex]\\left(-1,0\\right);m=\\Large\\frac{1}{5}[\/latex]\r\n\r\n[latex]\\left(-3,3\\right);m=2[\/latex]\r\n\r\n\"The\r\n\r\n[latex]\\left(-4,2\\right);m=4[\/latex]\r\n\r\n[latex]\\left(1,5\\right);m=-3[\/latex]\r\n\r\n\"The\r\n\r\n[latex]\\left(2,3\\right);m=-1[\/latex]\r\n\r\nSolve Slope Applications<\/strong>\r\nIn the following exercises, solve these slope applications.\r\n\r\nSlope of a roof<\/strong> A fairly easy way to determine the slope is to take a [latex]\\text{12-inch}[\/latex] level and set it on one end on the roof surface. Then take a tape measure or ruler, and measure from the other end of the level down to the roof surface. You can use these measurements to calculate the slope of the roof. What is the slope of the roof in this picture?\r\n\r\n\"A\r\n\r\n[latex]\\Large\\frac{1}{3}[\/latex]\r\n\r\nWhat is the slope of the roof shown?\r\n\r\n\"A\r\n\r\nRoad grade<\/strong> A local road has a grade of [latex]\\text{6%}[\/latex]. The grade of a road is its slope expressed as a percent.\r\n
      \r\n \t
    1. \u24d0 Find the slope of the road as a fraction and then simplify the fraction.<\/li>\r\n \t
    2. \u24d1 What rise and run would reflect this slope or grade?<\/li>\r\n<\/ol>\r\n\u24d0 [latex]\\Large\\frac{3}{50}[\/latex] \u24d1 [latex]\\text{rise}=3;\\text{run}=50[\/latex]\r\n\r\nHighway grade<\/strong> A local road rises [latex]2[\/latex] feet for every [latex]50[\/latex] feet of highway.\r\n
        \r\n \t
      1. \u24d0 What is the slope of the highway?<\/li>\r\n \t
      2. \u24d1 The grade of a highway is its slope expressed as a percent. What is the grade of this highway?<\/li>\r\n<\/ol>\r\n

        Everyday Math<\/h2>\r\nWheelchair ramp<\/strong> The rules for wheelchair ramps require a maximum [latex]1[\/latex] inch rise for a [latex]12[\/latex] inch run.\r\n
          \r\n \t
        1. \u24d0 How long must the ramp be to accommodate a [latex]\\text{24-inch}[\/latex] rise to the door?<\/li>\r\n \t
        2. \u24d1 Draw a model of this ramp.<\/li>\r\n<\/ol>\r\n\u24d0 288 inches (24 feet)\r\n\u24d1 Models will vary.\r\n\r\nWheelchair ramp<\/strong> A [latex]\\text{1-inch}[\/latex] rise for a [latex]\\text{16-inch}[\/latex] run makes it easier for the wheelchair rider to ascend the ramp.\r\n
            \r\n \t
          1. \u24d0 How long must the ramp be to easily accommodate a [latex]\\text{24-inch}[\/latex] rise to the door?<\/li>\r\n \t
          2. \u24d1 Draw a model of this ramp.<\/li>\r\n<\/ol>\r\n

            Writing Exercises<\/h2>\r\nWhat does the sign of the slope tell you about a line?\r\n\r\nAnswers will vary.\r\n\r\nHow does the graph of a line with slope [latex]m=\\Large\\frac{1}{2}[\/latex] differ from the graph of a line with slope [latex]m=2?[\/latex]\r\n\r\nWhy is the slope of a vertical line undefined?\r\n\r\nAnswers will vary.\r\n\r\nExplain how you can graph a line given a point and its slope.\r\n

            Self Check<\/h2>\r\n\u24d0 After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.\r\n\r\n\"Checklist\r\n\u24d1 On a scale of 1\u201310, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?\r\n

            Chapter Review Exercises<\/h1>\r\n

            Use the Rectangular Coordinate System<\/h2>\r\nPlot Points in a Rectangular Coordinate System<\/strong>\r\nIn the following exercises, plot each point in a rectangular coordinate system.\r\n\r\n[latex]\\left(1,3\\right),\\left(3,1\\right)[\/latex]\r\n\r\n\"The\r\n\r\n[latex]\\left(2,5\\right),\\left(5,2\\right)[\/latex]\r\n\r\nIn the following exercises, plot each point in a rectangular coordinate system and identify the quadrant in which the point is located.\r\n
              \r\n \t
            1. \u24d0 [latex]\\left(-1,-5\\right)[\/latex]<\/li>\r\n \t
            2. \u24d1 [latex]\\left(-3,4\\right)[\/latex]<\/li>\r\n \t
            3. \u24d2 [latex]\\left(2,-3\\right)[\/latex]<\/li>\r\n \t
            4. \u24d3 [latex]\\left(1,\\Large\\frac{5}{2}\\normalsize\\right)[\/latex]<\/li>\r\n<\/ol>\r\n\u24d0 III\r\n\u24d1 II\r\n\u24d2 IV\r\n\u24d0 I\r\n
                \r\n \t
              1. \u24d0 [latex]\\left(3,-2\\right)[\/latex]<\/li>\r\n \t
              2. \u24d1 [latex]\\left(-4,-1\\right)[\/latex]<\/li>\r\n \t
              3. \u24d2 [latex]\\left(-5,4\\right)[\/latex]<\/li>\r\n \t
              4. \u24d3 [latex]\\left(2,\\Large\\frac{10}{3}\\normalsize\\right)[\/latex]<\/li>\r\n<\/ol>\r\nIdentify Points on a Graph<\/strong>\r\nIn the following exercises, name the ordered pair of each point shown in the rectangular coordinate system.\r\n\r\n\"The\r\n\r\n\u24d0 (5,3)\r\n\u24d1 (2,\u22121)\r\n\u24d2 (\u22123,\u22122)\r\n\u24d3 (\u22121,4)\r\n\r\n\"The\r\n\r\n\"The\r\n\r\n\u24d0 (2,0)\r\n\u24d1 (0,\u22125)\r\n\u24d2 (\u22124,0)\r\n\u24d3 (0,3)\r\n\r\n\"The\r\n\r\nVerify Solutions to an Equation in Two Variables<\/strong>\r\nIn the following exercises, find the ordered pairs that are solutions to the given equation.\r\n\r\n[latex]5x+y=10[\/latex]\r\n
                  \r\n \t
                1. \u24d0 [latex]\\left(5,1\\right)[\/latex]<\/li>\r\n \t
                2. \u24d1 [latex]\\left(2,0\\right)[\/latex]<\/li>\r\n \t
                3. \u24d2 [latex]\\left(4,-10\\right)[\/latex]<\/li>\r\n<\/ol>\r\n\u24d1,\u24d2\r\n\r\n[latex]y=6x - 2[\/latex]\r\n
                    \r\n \t
                  1. \u24d0 [latex]\\left(1,4\\right)[\/latex]<\/li>\r\n \t
                  2. \u24d1 [latex]\\left(\\Large\\frac{1}{3}\\normalsize ,0\\right)[\/latex]<\/li>\r\n \t
                  3. \u24d2 [latex]\\left(6,-2\\right)[\/latex]<\/li>\r\n<\/ol>\r\nComplete a Table of Solutions to a Linear Equation in Two Variables<\/strong>\r\nIn the following exercises, complete the table to find solutions to each linear equation.\r\n\r\n[latex]y=4x - 1[\/latex]\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
                    [latex]x[\/latex]<\/th>\r\n[latex]y[\/latex]<\/th>\r\n[latex]\\left(x,y\\right)[\/latex]<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
                    [latex]0[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
                    [latex]1[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
                    [latex]-2[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
                    [latex]x[\/latex]<\/th>\r\n[latex]y[\/latex]<\/th>\r\n[latex]\\left(x,y\\right)[\/latex]<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
                    [latex]0[\/latex]<\/td>\r\n[latex]-1[\/latex]<\/td>\r\n[latex]\\left(0,-1\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
                    [latex]1[\/latex]<\/td>\r\n[latex]3[\/latex]<\/td>\r\n[latex]\\left(1,3\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
                    [latex]-2[\/latex]<\/td>\r\n[latex]-9[\/latex]<\/td>\r\n[latex]\\left(-2,-9\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[latex]y=-\\Large\\frac{1}{2}\\normalsize x+3[\/latex]\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
                    [latex]x[\/latex]<\/th>\r\n[latex]y[\/latex]<\/th>\r\n[latex]\\left(x,y\\right)[\/latex]<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
                    [latex]0[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
                    [latex]1[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
                    [latex]-2[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[latex]x+2y=5[\/latex]\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
                    [latex]x[\/latex]<\/th>\r\n[latex]y[\/latex]<\/th>\r\n[latex]\\left(x,y\\right)[\/latex]<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
                    <\/td>\r\n[latex]0[\/latex]<\/td>\r\n<\/td>\r\n<\/tr>\r\n
                    [latex]1[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
                    [latex]-1[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
                    [latex]x[\/latex]<\/th>\r\n[latex]y[\/latex]<\/th>\r\n[latex]\\left(x,y\\right)[\/latex]<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
                    [latex]5[\/latex]<\/td>\r\n[latex]0[\/latex]<\/td>\r\n[latex]\\left(5,0\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
                    [latex]1[\/latex]<\/td>\r\n[latex]2[\/latex]<\/td>\r\n[latex]\\left(1,2\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
                    [latex]-1[\/latex]<\/td>\r\n[latex]3[\/latex]<\/td>\r\n[latex]\\left(-1,3\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[latex]3x - 2y=6[\/latex]\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
                    [latex]x[\/latex]<\/th>\r\n[latex]y[\/latex]<\/th>\r\n[latex]\\left(x,y\\right)[\/latex]<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
                    [latex]0[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
                    <\/td>\r\n[latex]0[\/latex]<\/td>\r\n<\/td>\r\n<\/tr>\r\n
                    [latex]-2[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nFind Solutions to a Linear Equation in Two Variables<\/strong>\r\nIn the following exercises, find three solutions to each linear equation.\r\n\r\n[latex]x+y=3[\/latex]\r\n\r\nAnswers will vary.\r\n\r\n[latex]x+y=-4[\/latex]\r\n\r\n[latex]y=3x+1[\/latex]\r\n\r\nAnswers will vary.\r\n\r\n[latex]y=-x - 1[\/latex]\r\n

                    Graphing Linear Equations<\/h2>\r\nRecognize the Relation Between the Solutions of an Equation and its Graph<\/strong>\r\nIn the following exercises, for each ordered pair, decide\r\n\r\n\u24d0 if the ordered pair is a solution to the equation.\r\n\u24d1 if the point is on the line.\r\n\r\n[latex]y=-x+4[\/latex]\r\n
                      \r\n \t
                    1. \u24d0 [latex]\\left(0,4\\right)[\/latex]<\/li>\r\n \t
                    2. \u24d1 [latex]\\left(-1,3\\right)[\/latex]<\/li>\r\n \t
                    3. \u24d2 [latex]\\left(2,2\\right)[\/latex]<\/li>\r\n \t
                    4. \u24d3 [latex]\\left(-2,6\\right)[\/latex]<\/li>\r\n<\/ol>\r\n\"The\r\n\r\n\u24d0 yes \u24d1 no \u24d2 yes \u24d3 yes\r\n\u24d0 yes \u24d1 no \u24d2 yes \u24d3 yes\r\n\r\n[latex]y=\\Large\\frac{2}{3}\\normalsize x - 1[\/latex]\r\n
                        \r\n \t
                      1. \u24d0 [latex]\\left(0,-1\\right)[\/latex]<\/li>\r\n \t
                      2. \u24d1 [latex]\\left(3,1\\right)[\/latex]<\/li>\r\n \t
                      3. \u24d2 [latex]\\left(-3,-3\\right)[\/latex]<\/li>\r\n \t
                      4. \u24d3 [latex]\\left(6,4\\right)[\/latex]<\/li>\r\n<\/ol>\r\n\"The\r\n\r\nGraph a Linear Equation by Plotting Points<\/strong>\r\nIn the following exercises, graph by plotting points.\r\n\r\n[latex]y=4x - 3[\/latex]\r\n\r\n\"The\r\n\r\n[latex]y=-3x[\/latex]\r\n\r\n[latex]2x+y=7[\/latex]\r\n\r\n\"The\r\n\r\nGraph Vertical and Horizontal lines<\/strong>\r\nIn the following exercises, graph the vertical or horizontal lines.\r\n\r\n[latex]y=-2[\/latex]\r\n\r\n[latex]x=3[\/latex]\r\n\r\n\"The\r\n

                        Graphing with Intercepts<\/h2>\r\nIdentify the Intercepts on a Graph<\/strong>\r\nIn the following exercises, find the [latex]x\\text{-}[\/latex] and [latex]y\\text{-intercepts}[\/latex].\r\n\r\n\"The\r\n\r\n\"The\r\n\r\n(0,3) (3,0)\r\n\r\nFind the Intercepts from an Equation of a Line<\/strong>\r\nIn the following exercises, find the intercepts.\r\n\r\n[latex]x+y=5[\/latex]\r\n\r\n[latex]x-y=-1[\/latex]\r\n\r\n(\u22121,0) (0,1)\r\n\r\n[latex]y=\\Large\\frac{3}{4}\\normalsize x - 12[\/latex]\r\n\r\n[latex]y=3x[\/latex]\r\n\r\n(0,0)\r\n\r\nGraph a Line Using the Intercepts<\/strong>\r\nIn the following exercises, graph using the intercepts.\r\n\r\n[latex]-x+3y=3[\/latex]\r\n\r\n[latex]x+y=-2[\/latex]\r\n\r\n\"This\r\n\r\nChoose the Most Convenient Method to Graph a Line<\/strong>\r\nIn the following exercises, identify the most convenient method to graph each line.\r\n\r\n[latex]x=5[\/latex]\r\n\r\n[latex]y=-3[\/latex]\r\n\r\nhorizontal line\r\n\r\n[latex]2x+y=5[\/latex]\r\n\r\n[latex]x-y=2[\/latex]\r\n\r\nintercepts\r\n\r\n[latex]y=\\Large\\frac{1}{2}\\normalsize x+2[\/latex]\r\n\r\n[latex]y=\\Large\\frac{3}{4}\\normalsize x - 1[\/latex]\r\n\r\nplotting points\r\n

                        Understand Slope of a Line<\/h2>\r\nUse Geoboards to Model Slope<\/strong>\r\nIn the following exercises, find the slope modeled on each geoboard.\r\n\r\n\"The\r\n\r\n\"The\r\n\r\n[latex]\\Large\\frac{4}{3}[\/latex]\r\n\r\n\"The\r\n\r\n\"The\r\n\r\n[latex]-\\Large\\frac{2}{3}[\/latex]\r\n\r\nIn the following exercises, model each slope. Draw a picture to show your results.\r\n\r\n[latex]\\Large\\frac{1}{3}[\/latex]\r\n\r\n[latex]\\Large\\frac{3}{2}[\/latex]\r\n\r\n\"The\r\n\r\n[latex]-\\Large\\frac{2}{3}[\/latex]\r\n\r\n[latex]-\\Large\\frac{1}{2}[\/latex]\r\n\r\n\"The\r\n\r\nFind the Slope of a Line from its Graph<\/strong>\r\nIn the following exercises, find the slope of each line shown.\r\n\r\n\"The\r\n\r\n\"The\r\n\r\n1\r\n\r\n\"The\r\n\r\n\"The\r\n\r\n[latex]-\\Large\\frac{1}{2}[\/latex]\r\n\r\nFind the Slope of Horizontal and Vertical Lines<\/strong>\r\nIn the following exercises, find the slope of each line.\r\n\r\n[latex]y=2[\/latex]\r\n\r\n[latex]x=5[\/latex]\r\n\r\nundefined\r\n\r\n[latex]x=-3[\/latex]\r\n\r\n[latex]y=-1[\/latex]\r\n\r\n0\r\n\r\nUse the Slope Formula to find the Slope of a Line between Two Points<\/strong>\r\nIn the following exercises, use the slope formula to find the slope of the line between each pair of points.\r\n\r\n[latex]\\left(2,1\\right),\\left(4,5\\right)[\/latex]\r\n\r\n[latex]\\left(-1,-1\\right),\\left(0,-5\\right)[\/latex]\r\n\r\n\u22124\r\n\r\n[latex]\\left(3,5\\right),\\left(4,-1\\right)[\/latex]\r\n\r\n[latex]\\left(-5,-2\\right),\\left(3,2\\right)[\/latex]\r\n\r\n[latex]\\Large\\frac{1}{2}[\/latex]\r\n\r\nGraph a Line Given a Point and the Slope<\/strong>\r\nIn the following exercises, graph the line given a point and the slope.\r\n\r\n[latex]\\left(2,-2\\right);m=\\Large\\frac{5}{2}[\/latex]\r\n\r\n[latex]\\left(-3,4\\right);m=-\\Large\\frac{1}{3}[\/latex]\r\n\r\n\"The\r\n\r\nSolve Slope Applications<\/strong>\r\nIn the following exercise, solve the slope application.\r\n\r\nA roof has rise [latex]10[\/latex] feet and run [latex]15[\/latex] feet. What is its slope?\r\n

                        Chapter Practice Test<\/h1>\r\nPlot and label these points:\r\n
                          \r\n \t
                        1. \u24d0 [latex]\\left(2,5\\right)[\/latex]<\/li>\r\n \t
                        2. \u24d1 [latex]\\left(-1,-3\\right)[\/latex]<\/li>\r\n \t
                        3. \u24d2 [latex]\\left(-4,0\\right)[\/latex]<\/li>\r\n \t
                        4. \u24d3 [latex]\\left(3,-5\\right)[\/latex]<\/li>\r\n \t
                        5. \u24d4 [latex]\\left(-2,1\\right)[\/latex]<\/li>\r\n<\/ol>\r\n\"The\r\n\r\nName the ordered pair for each point shown.\r\n\r\n\"The\r\n\r\nFind the [latex]x\\text{-intercept}[\/latex] and [latex]y\\text{-intercept}[\/latex] on the line shown.\r\n\r\n\"The\r\n\r\n(4,0), (0,\u22122)\r\n\r\nFind the [latex]x\\text{-intercept}[\/latex] and [latex]y\\text{-intercept}[\/latex] of the equation [latex]3x-y=6[\/latex].\r\n\r\nIs [latex]\\left(1,3\\right)[\/latex] a solution to the equation [latex]x+4y=12?[\/latex] How do you know?\r\n\r\nno; 1 + 4 \u00b7 3 \u2260 12\r\n\r\nComplete the table to find four solutions to the equation [latex]y=-x+1[\/latex].\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
                          [latex]x[\/latex]<\/td>\r\n[latex]y[\/latex]<\/td>\r\n[latex]\\left(x,y\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
                          [latex]0[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
                          [latex]1[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
                          [latex]3[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
                          [latex]-2[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nComplete the table to find three solutions to the equation [latex]4x+y=8[\/latex]\r\n\r\n\r\n\r\n\r\n\r\n\r\n
                          [latex]x[\/latex]<\/td>\r\n[latex]y[\/latex]<\/td>\r\n[latex]\\left(x,y\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
                          [latex]0[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
                          <\/td>\r\n[latex]0[\/latex]<\/td>\r\n<\/td>\r\n<\/tr>\r\n
                          [latex]3[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n\r\n\r\n\r\n\r\n\r\n
                          [latex]x[\/latex]<\/td>\r\n[latex]y[\/latex]<\/td>\r\n[latex]\\left(x,y\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
                          [latex]0[\/latex]<\/td>\r\n[latex]8[\/latex]<\/td>\r\n[latex]\\left(0,8\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
                          [latex]2[\/latex]<\/td>\r\n[latex]0[\/latex]<\/td>\r\n[latex]\\left(2,0\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
                          [latex]3[\/latex]<\/td>\r\n[latex]-4[\/latex]<\/td>\r\n[latex]\\left(3,-4\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nIn the following exercises, find three solutions to each equation and then graph each line.\r\n\r\n[latex]y=-3x[\/latex]\r\n\r\n[latex]2x+3y=-6[\/latex]\r\n\r\n\"\r\n\r\nIn the following exercises, find the slope of each line.\r\n\r\n\"The\r\n\r\n\"The\r\n\r\n[latex]-\\Large\\frac{5}{2}[\/latex]\r\n\r\nUse the slope formula to find the slope of the line between [latex]\\left(0,-4\\right)[\/latex] and [latex]\\left(5,2\\right)[\/latex].\r\n\r\nFind the slope of the line [latex]y=2[\/latex].\r\n\r\n0\r\n\r\nGraph the line passing through [latex]\\left(1,1\\right)[\/latex] with slope [latex]m=\\Large\\frac{3}{2}[\/latex].\r\n\r\nA bicycle route climbs [latex]20[\/latex] feet for [latex]1,000[\/latex] feet of horizontal distance. What is the slope of the route?\r\n\r\n[latex]\\Large\\frac{1}{50}[\/latex]","rendered":"

                          Practice Makes Perfect<\/h2>\n

                          Plot Points on a Rectangular Coordinate System<\/strong>
                          \nIn the following exercises, plot each point on a coordinate grid.<\/p>\n

                          [latex]\\left(3,2\\right)[\/latex]<\/p>\n

                          \"The<\/p>\n

                          [latex]\\left(4,1\\right)[\/latex]<\/p>\n

                          [latex]\\left(1,5\\right)[\/latex]<\/p>\n

                          \"The<\/p>\n

                          [latex]\\left(3,4\\right)[\/latex]<\/p>\n

                          [latex]\\left(4,1\\right),\\left(1,4\\right)[\/latex]<\/p>\n

                          \"The<\/p>\n

                          [latex]\\left(3,2\\right),\\left(2,3\\right)[\/latex]<\/p>\n

                          [latex]\\left(3,4\\right),\\left(4,3\\right)[\/latex]<\/p>\n

                          \"The<\/p>\n

                          In the following exercises, plot each point on a coordinate grid and identify the quadrant in which the point is located.<\/p>\n

                          \u24d0 [latex]\\left(-4,2\\right)[\/latex]
                          \n\u24d1 [latex]\\left(-1,-2\\right)[\/latex]
                          \n\u24d2 [latex]\\left(3,-5\\right)[\/latex]
                          \n\u24d3 [latex]\\left(2,\\Large\\frac{5}{2}\\normalsize\\right)[\/latex]<\/p>\n

                          \u24d0 [latex]\\left(-2,-3\\right)[\/latex]
                          \n\u24d1 [latex]\\left(3,-3\\right)[\/latex]
                          \n\u24d2 [latex]\\left(-4,1\\right)[\/latex]
                          \n\u24d3 [latex]\\left(1,\\Large\\frac{3}{2}\\normalsize\\right)[\/latex]<\/p>\n

                          \"The<\/p>\n

                          \u24d0 [latex]\\left(-1,1\\right)[\/latex]
                          \n\u24d1 [latex]\\left(-2,-1\\right)[\/latex]
                          \n\u24d2 [latex]\\left(1,-4\\right)[\/latex]
                          \n\u24d3 [latex]\\left(3,\\Large\\frac{7}{2}\\normalsize\\right)[\/latex]<\/p>\n

                          \u24d0 [latex]\\left(3,-2\\right)[\/latex]
                          \n\u24d1 [latex]\\left(-3,2\\right)[\/latex]
                          \n\u24d2 [latex]\\left(-3,-2\\right)[\/latex]
                          \n\u24d3 [latex]\\left(3,2\\right)[\/latex]<\/p>\n

                          \"The<\/p>\n

                          \u24d0 [latex]\\left(4,-1\\right)[\/latex]
                          \n\u24d1 [latex]\\left(-4,1\\right)[\/latex]
                          \n\u24d2 [latex]\\left(-4,-1\\right)[\/latex]
                          \n\u24d3 [latex]\\left(4,1\\right)[\/latex]<\/p>\n

                          \u24d0 [latex]\\left(-2,0\\right)[\/latex]
                          \n\u24d1 [latex]\\left(-3,0\\right)[\/latex]
                          \n\u24d2 [latex]\\left(0,4\\right)[\/latex]
                          \n\u24d3 [latex]\\left(0,2\\right)[\/latex]<\/p>\n

                          \"The<\/p>\n

                          Identify Points on a Graph<\/strong>
                          \nIn the following exercises, name the ordered pair of each point shown.<\/p>\n

                          \"The<\/p>\n

                          \"TThe<\/p>\n

                          \"The<\/p>\n

                          \"The<\/p>\n

                          \"The<\/p>\n

                          \"The<\/p>\n

                          \"The<\/p>\n

                          Verify Solutions to an Equation in Two Variables<\/strong>
                          \nIn the following exercises, determine which ordered pairs are solutions to the given equation.<\/p>\n

                          [latex]2x+y=6[\/latex]<\/p>\n

                          \u24d0 [latex]\\left(1,4\\right)[\/latex]
                          \n\u24d1 [latex]\\left(3,0\\right)[\/latex]
                          \n\u24d2 [latex]\\left(2,3\\right)[\/latex]<\/p>\n

                          \u24d0, \u24d1<\/p>\n

                          [latex]x+3y=9[\/latex]<\/p>\n

                            \n
                          1. \u24d0 [latex]\\left(0,3\\right)[\/latex]<\/li>\n
                          2. \u24d1 [latex]\\left(6,1\\right)[\/latex]<\/li>\n
                          3. \u24d2 [latex]\\left(-3,-3\\right)[\/latex]<\/li>\n<\/ol>\n

                            [latex]4x - 2y=8[\/latex]<\/p>\n

                            \u24d0 [latex]\\left(3,2\\right)[\/latex]
                            \n\u24d1 [latex]\\left(1,4\\right)[\/latex]
                            \n\u24d2 [latex]\\left(0,-4\\right)[\/latex]<\/p>\n

                            \u24d0, \u24d2<\/p>\n

                            [latex]3x - 2y=12[\/latex]<\/p>\n

                            \u24d0 [latex]\\left(4,0\\right)[\/latex]
                            \n\u24d1 [latex]\\left(2,-3\\right)[\/latex]
                            \n\u24d2 [latex]\\left(1,6\\right)[\/latex]<\/p>\n

                            [latex]y=4x+3[\/latex]<\/p>\n

                            \u24d0 [latex]\\left(4,3\\right)[\/latex]
                            \n\u24d1 [latex]\\left(-1,-1\\right)[\/latex]
                            \n\u24d2 [latex]\\left(\\Large\\frac{1}{2}\\normalsize,5\\right)[\/latex]<\/p>\n

                            \u24d1, \u24d2<\/p>\n

                            [latex]y=2x - 5[\/latex]<\/p>\n

                            \u24d0 [latex]\\left(0,-5\\right)[\/latex]
                            \n\u24d1 [latex]\\left(2,1\\right)[\/latex]
                            \n\u24d2 [latex]\\left(\\Large\\frac{1}{2}\\normalsize ,-4\\right)[\/latex]<\/p>\n

                            [latex]y=\\Large\\frac{1}{2}\\normalsize x - 1[\/latex]<\/p>\n

                            \u24d0 [latex]\\left(2,0\\right)[\/latex]
                            \n\u24d1 [latex]\\left(-6,-4\\right)[\/latex]
                            \n\u24d2 [latex]\\left(-4,-1\\right)[\/latex]<\/p>\n

                            \u24d0, \u24d1<\/p>\n

                            [latex]y=\\Large\\frac{1}{3}\\normalsize x+1[\/latex]<\/p>\n

                            \u24d0 [latex]\\left(-3,0\\right)[\/latex]
                            \n\u24d1 [latex]\\left(9,4\\right)[\/latex]
                            \n\u24d2 [latex]\\left(-6,-1\\right)[\/latex]<\/p>\n

                            Find Solutions to Linear Equations in Two Variables<\/strong>
                            \nIn the following exercises, complete the table to find solutions to each linear equation.<\/p>\n

                            [latex]y=2x - 4[\/latex]<\/p>\n\n\n\n\n\n\n\n
                            [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n[latex]\\left(x,y\\right)[\/latex]<\/th>\n<\/tr>\n<\/thead>\n
                            [latex]-1[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
                            [latex]0[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
                            [latex]2[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n\n\n
                            [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n[latex]\\left(x,y\\right)[\/latex]<\/th>\n<\/tr>\n<\/thead>\n
                            [latex]-1[\/latex]<\/td>\n[latex]-6[\/latex]<\/td>\n[latex]\\left(-1,-6\\right)[\/latex]<\/td>\n<\/tr>\n
                            [latex]0[\/latex]<\/td>\n[latex]-4[\/latex]<\/td>\n[latex]\\left(0,-4\\right)[\/latex]<\/td>\n<\/tr>\n
                            [latex]2[\/latex]<\/td>\n[latex]0[\/latex]<\/td>\n[latex]\\left(2,0\\right)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                            [latex]y=3x - 1[\/latex]<\/p>\n\n\n\n\n\n\n\n
                            [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n[latex]\\left(x,y\\right)[\/latex]<\/th>\n<\/tr>\n<\/thead>\n
                            [latex]-1[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
                            [latex]0[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
                            [latex]2[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                            [latex]y=-x+5[\/latex]<\/p>\n\n\n\n\n\n\n\n
                            [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n[latex]\\left(x,y\\right)[\/latex]<\/th>\n<\/tr>\n<\/thead>\n
                            [latex]-2[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
                            [latex]0[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
                            [latex]3[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n\n\n
                            [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n[latex]\\left(x,y\\right)[\/latex]<\/th>\n<\/tr>\n<\/thead>\n
                            [latex]-2[\/latex]<\/td>\n[latex]7[\/latex]<\/td>\n[latex]\\left(-2,7\\right)[\/latex]<\/td>\n<\/tr>\n
                            [latex]0[\/latex]<\/td>\n[latex]5[\/latex]<\/td>\n[latex]\\left(0,5\\right)[\/latex]<\/td>\n<\/tr>\n
                            [latex]3[\/latex]<\/td>\n[latex]2[\/latex]<\/td>\n[latex]\\left(3,2\\right)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                            [latex]y=\\Large\\frac{1}{3}\\normalsize x+1[\/latex]<\/p>\n\n\n\n\n\n\n\n
                            [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n[latex]\\left(x,y\\right)[\/latex]<\/th>\n<\/tr>\n<\/thead>\n
                            [latex]0[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
                            [latex]3[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
                            [latex]6[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                            [latex]y=-\\Large\\frac{3}{2}\\normalsize x - 2[\/latex]<\/p>\n\n\n\n\n\n\n\n
                            [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n[latex]\\left(x,y\\right)[\/latex]<\/th>\n<\/tr>\n<\/thead>\n
                            [latex]-2[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
                            [latex]0[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
                            [latex]2[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n\n\n
                            [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n[latex]\\left(x,y\\right)[\/latex]<\/th>\n<\/tr>\n<\/thead>\n
                            [latex]-2[\/latex]<\/td>\n[latex]1[\/latex]<\/td>\n[latex]\\left(-2,1\\right)[\/latex]<\/td>\n<\/tr>\n
                            [latex]0[\/latex]<\/td>\n[latex]-2[\/latex]<\/td>\n[latex]\\left(0,-2\\right)[\/latex]<\/td>\n<\/tr>\n
                            [latex]2[\/latex]<\/td>\n[latex]-5[\/latex]<\/td>\n[latex]\\left(2,-5\\right)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                            [latex]x+2y=8[\/latex]<\/p>\n\n\n\n\n\n\n\n
                            [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n[latex]\\left(x,y\\right)[\/latex]<\/th>\n<\/tr>\n<\/thead>\n
                            [latex]0[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
                            [latex]4[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
                            <\/td>\n[latex]0[\/latex]<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                            Everyday Math<\/h2>\n

                            Weight of a baby<\/strong> Mackenzie recorded her baby\u2019s weight every two months. The baby\u2019s age, in months, and weight, in pounds, are listed in the table, and shown as an ordered pair in the third column.
                            \n\u24d0 Plot the points on a coordinate grid.<\/p>\n\n\n\n\n\n\n\n\n\n\n
                            [latex]\\text{Age}[\/latex]<\/td>\n[latex]\\text{Weight}[\/latex]<\/td>\n[latex]\\left(x,y\\right)[\/latex]<\/td>\n<\/tr>\n
                            [latex]0[\/latex]<\/td>\n[latex]7[\/latex]<\/td>\n[latex]\\left(0,7\\right)[\/latex]<\/td>\n<\/tr>\n
                            [latex]2[\/latex]<\/td>\n[latex]11[\/latex]<\/td>\n[latex]\\left(2,11\\right)[\/latex]<\/td>\n<\/tr>\n
                            [latex]4[\/latex]<\/td>\n[latex]15[\/latex]<\/td>\n[latex]\\left(4,15\\right)[\/latex]<\/td>\n<\/tr>\n
                            [latex]6[\/latex]<\/td>\n[latex]16[\/latex]<\/td>\n[latex]\\left(6,16\\right)[\/latex]<\/td>\n<\/tr>\n
                            [latex]8[\/latex]<\/td>\n[latex]19[\/latex]<\/td>\n[latex]\\left(8,19\\right)[\/latex]<\/td>\n<\/tr>\n
                            [latex]10[\/latex]<\/td>\n[latex]20[\/latex]<\/td>\n[latex]\\left(10,20\\right)[\/latex]<\/td>\n<\/tr>\n
                            [latex]12[\/latex]<\/td>\n[latex]21[\/latex]<\/td>\n[latex]\\left(12,21\\right)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                            \u24d1 Why is only Quadrant I needed?<\/p>\n

                            \u24d0<\/p>\n

                            \"This
                            \n\u24d1 Age and weight are only positive.<\/p>\n

                            Weight of a child<\/strong> Latresha recorded her son\u2019s height and weight every year. His height, in inches, and weight, in pounds, are listed in the table, and shown as an ordered pair in the third column.
                            \n\u24d0 Plot the points on a coordinate grid.<\/p>\n\n\n\n\n\n\n\n\n\n
                            [latex]\\begin{array}{c}\\text{Height}\\hfill \\\\ x\\hfill \\end{array}[\/latex]<\/td>\n[latex]\\begin{array}{c}\\text{Weight}\\hfill \\\\ y\\hfill \\end{array}[\/latex]<\/td>\n[latex]\\begin{array}{}\\\\ \\left(x,y\\right)\\hfill \\end{array}[\/latex]<\/td>\n<\/tr>\n
                            [latex]28[\/latex]<\/td>\n[latex]22[\/latex]<\/td>\n[latex]\\left(28,22\\right)[\/latex]<\/td>\n<\/tr>\n
                            [latex]31[\/latex]<\/td>\n[latex]27[\/latex]<\/td>\n[latex]\\left(31,27\\right)[\/latex]<\/td>\n<\/tr>\n
                            [latex]33[\/latex]<\/td>\n[latex]33[\/latex]<\/td>\n[latex]\\left(33,33\\right)[\/latex]<\/td>\n<\/tr>\n
                            [latex]37[\/latex]<\/td>\n[latex]35[\/latex]<\/td>\n[latex]\\left(37,35\\right)[\/latex]<\/td>\n<\/tr>\n
                            [latex]40[\/latex]<\/td>\n[latex]41[\/latex]<\/td>\n[latex]\\left(40,41\\right)[\/latex]<\/td>\n<\/tr>\n
                            [latex]42[\/latex]<\/td>\n[latex]45[\/latex]<\/td>\n[latex]\\left(42,45\\right)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                            \u24d1 Why is only Quadrant I needed?<\/p>\n

                            Writing Exercises<\/h2>\n

                            Have you ever used a map with a rectangular coordinate system? Describe the map and how you used it.<\/p>\n

                            Answers may vary.<\/p>\n

                            How do you determine if an ordered pair is a solution to a given equation?<\/p>\n

                            Self Check<\/h2>\n

                            \u24d0 After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.<\/p>\n

                            \"Checklist
                            \n\u24d1 If most of your checks were:
                            \n\u2026confidently. Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific.
                            \n\u2026with some help. This must be addressed quickly because topics you do not master become potholes in your road to success. In math, every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Who can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?
                            \n\u2026no\u2014I don\u2019t get it! This is a warning sign and you must not ignore it. You should get help right away or you will quickly be overwhelmed. See your instructor as soon as you can to discuss your situation. Together<\/p>\n

                             <\/p>\n

                             <\/p>\n

                            Practice Makes Perfect<\/h2>\n

                            Identify the Intercepts on a Graph<\/strong>
                            \nIn the following exercises, find the [latex]x\\text{-}[\/latex] and [latex]y\\text{-}[\/latex] intercepts.<\/p>\n

                            \"The<\/p>\n

                            (3,0),(0,3)<\/p>\n

                            \"The<\/p>\n

                            \"The<\/p>\n

                            (5,0),(0,\u22125)<\/p>\n

                            \"The<\/p>\n

                            \"The<\/p>\n

                            (\u22122,0),(0,\u22122)<\/p>\n

                            \"The<\/p>\n

                            \"The<\/p>\n

                            (\u22121,0),(0,1)<\/p>\n

                            \"The<\/p>\n

                            \"The<\/p>\n

                            (0,0)<\/p>\n

                            \"The<\/p>\n

                            Find the [latex]x[\/latex] and [latex]y[\/latex] Intercepts from an Equation of a Line<\/strong>
                            \nIn the following exercises, find the intercepts.<\/p>\n

                            [latex]x+y=4[\/latex]<\/p>\n

                            (4,0),(0,4)<\/p>\n

                            [latex]x+y=3[\/latex]<\/p>\n

                            [latex]x+y=-2[\/latex]<\/p>\n

                            (\u22122,0),(0,\u22122)<\/p>\n

                            [latex]x+y=-5[\/latex]<\/p>\n

                            [latex]x-y=5[\/latex]<\/p>\n

                            (5,0),(0,\u22125)<\/p>\n

                            [latex]x-y=1[\/latex]<\/p>\n

                            [latex]x-y=-3[\/latex]<\/p>\n

                            (\u22123,0),(0,3)<\/p>\n

                            [latex]x-y=-4[\/latex]<\/p>\n

                            [latex]x+2y=8[\/latex]<\/p>\n

                            (8,0),(0,4)<\/p>\n

                            [latex]x+2y=10[\/latex]<\/p>\n

                            [latex]3x+y=6[\/latex]<\/p>\n

                            (2,0),(0,6)<\/p>\n

                            [latex]3x+y=9[\/latex]<\/p>\n

                            [latex]x - 3y=12[\/latex]<\/p>\n

                            (12,0),(0,\u22124)<\/p>\n

                            [latex]x - 2y=8[\/latex]<\/p>\n

                            [latex]4x-y=8[\/latex]<\/p>\n

                            (2,0),(0,\u22128)<\/p>\n

                            [latex]5x-y=5[\/latex]<\/p>\n

                            [latex]2x+5y=10[\/latex]<\/p>\n

                            (5,0),(0,2)<\/p>\n

                            [latex]2x+3y=6[\/latex]<\/p>\n

                            [latex]3x - 2y=12[\/latex]<\/p>\n

                            (4,0),(0,\u22126)<\/p>\n

                            [latex]3x - 5y=30[\/latex]<\/p>\n

                            [latex]y=\\Large\\frac{1}{3}\\normalsize x - 1[\/latex]<\/p>\n

                            (3,0),(0,\u22121)<\/p>\n

                            [latex]y=\\Large\\frac{1}{4}\\normalsize x - 1[\/latex]<\/p>\n

                            [latex]y=\\Large\\frac{1}{5}\\normalsize x+2[\/latex]<\/p>\n

                            (\u221210,0),(0,2)<\/p>\n

                            [latex]y=\\Large\\frac{1}{3}\\normalsize x+4[\/latex]<\/p>\n

                            [latex]y=3x[\/latex]<\/p>\n

                            (0,0)<\/p>\n

                            [latex]y=-2x[\/latex]<\/p>\n

                            [latex]y=-4x[\/latex]<\/p>\n

                            (0,0)<\/p>\n

                            [latex]y=5x[\/latex]<\/p>\n

                            Graph a Line Using the Intercepts<\/strong>
                            \nIn the following exercises, graph using the intercepts.<\/p>\n

                            [latex]-x+5y=10[\/latex]<\/p>\n

                            \"The<\/p>\n

                            [latex]-x+4y=8[\/latex]<\/p>\n

                            [latex]x+2y=4[\/latex]<\/p>\n

                            \"The<\/p>\n

                            [latex]x+2y=6[\/latex]<\/p>\n

                            [latex]x+y=2[\/latex]<\/p>\n

                            \"The<\/p>\n

                            [latex]x+y=5[\/latex]<\/p>\n

                            [latex]x+y=-3[\/latex]<\/p>\n

                            \"The<\/p>\n

                            [latex]x+y=-1[\/latex]<\/p>\n

                            [latex]x-y=1[\/latex]<\/p>\n

                            \"The<\/p>\n

                            [latex]x-y=2[\/latex]<\/p>\n

                            [latex]x-y=-4[\/latex]<\/p>\n

                            \"The<\/p>\n

                            [latex]x-y=-3[\/latex]<\/p>\n

                            [latex]4x+y=4[\/latex]<\/p>\n

                            \"The<\/p>\n

                            [latex]3x+y=3[\/latex]<\/p>\n

                            [latex]3x-y=-6[\/latex]<\/p>\n

                            \"The<\/p>\n

                            [latex]2x-y=-8[\/latex]<\/p>\n

                            [latex]2x+4y=12[\/latex]<\/p>\n

                            \"The<\/p>\n

                            [latex]3x+2y=12[\/latex]<\/p>\n

                            [latex]3x - 2y=6[\/latex]<\/p>\n

                            \"The<\/p>\n

                            [latex]5x - 2y=10[\/latex]<\/p>\n

                            [latex]2x - 5y=-20[\/latex]<\/p>\n

                            \"The<\/p>\n

                            [latex]3x - 4y=-12[\/latex]<\/p>\n

                            [latex]y=-2x[\/latex]<\/p>\n

                            \"The<\/p>\n

                            [latex]y=-4x[\/latex]<\/p>\n

                            [latex]y=x[\/latex]<\/p>\n

                            \"The<\/p>\n

                            [latex]y=3x[\/latex]<\/p>\n

                            Choose the Most Convenient Method to Graph a Line<\/strong>
                            \nIn the following exercises, identify the most convenient method to graph each line.<\/p>\n

                            [latex]x=2[\/latex]<\/p>\n

                            vertical line<\/p>\n

                            [latex]y=4[\/latex]<\/p>\n

                            [latex]y=5[\/latex]<\/p>\n

                            horizontal line<\/p>\n

                            [latex]x=-3[\/latex]<\/p>\n

                            [latex]y=-3x+4[\/latex]<\/p>\n

                            plotting points<\/p>\n

                            [latex]y=-5x+2[\/latex]<\/p>\n

                            [latex]x-y=5[\/latex]<\/p>\n

                            intercepts<\/p>\n

                            [latex]x-y=1[\/latex]<\/p>\n

                            [latex]y=\\Large\\frac{2}{3}\\normalsize x - 1[\/latex]<\/p>\n

                            plotting points<\/p>\n

                            [latex]y=\\Large\\frac{4}{5}\\normalsize x - 3[\/latex]<\/p>\n

                            [latex]y=-3[\/latex]<\/p>\n

                            horizontal line<\/p>\n

                            [latex]y=-1[\/latex]<\/p>\n

                            [latex]3x - 2y=-12[\/latex]<\/p>\n

                            intercepts<\/p>\n

                            [latex]2x - 5y=-10[\/latex]<\/p>\n

                            [latex]y=-\\Large\\frac{1}{4}\\normalsize x+3[\/latex]<\/p>\n

                            plotting points<\/p>\n

                            [latex]y=-\\Large\\frac{1}{3}\\normalsize x+5[\/latex]<\/p>\n

                            Everyday Math<\/h2>\n

                            Road trip<\/strong> Damien is driving from Chicago to Denver, a distance of [latex]1,000[\/latex] miles. The [latex]x\\text{-axis}[\/latex] on the graph below shows the time in hours since Damien left Chicago. The [latex]y\\text{-axis}[\/latex] represents the distance he has left to drive.<\/p>\n

                            \"The
                            \n\u24d0 Find the [latex]x\\text{-}[\/latex] and [latex]y\\text{-}[\/latex] intercepts
                            \n\u24d1 Explain what the [latex]x\\text{-}[\/latex] and [latex]y\\text{-}[\/latex] intercepts mean for Damien.<\/p>\n

                            \u24d0 (0,1,000),(15,0). \u24d1 At (0,1,000) he left Chicago 0 hours ago and has 1,000 miles left to drive. At (15,0) he left Chicago 15 hours ago and has 0 miles left to drive.<\/p>\n

                            Road trip<\/strong> Ozzie filled up the gas tank of his truck and went on a road trip. The [latex]x\\text{-axis}[\/latex] on the graph shows the number of miles Ozzie drove since filling up. The [latex]y\\text{-axis}[\/latex] represents the number of gallons of gas in the truck\u2019s gas tank.<\/p>\n

                            \"The
                            \n\u24d0 Find the [latex]x\\text{-}[\/latex] and [latex]y\\text{-}[\/latex] intercepts.
                            \n\u24d1 Explain what the [latex]x\\text{-}[\/latex] and [latex]y\\text{-}[\/latex] intercepts mean for Ozzie.<\/p>\n

                            Writing Exercises<\/h2>\n

                            How do you find the [latex]x\\text{-intercept}[\/latex] of the graph of [latex]3x - 2y=6?[\/latex]<\/p>\n

                            Answers will vary.<\/p>\n

                            How do you find the [latex]y\\text{-intercept}[\/latex] of the graph of [latex]5x-y=10?[\/latex]<\/p>\n

                            Do you prefer to graph the equation [latex]4x+y=-4[\/latex] by plotting points or intercepts? Why?<\/p>\n

                            Answers will vary.<\/p>\n

                            Do you prefer to graph the equation [latex]y=\\Large\\frac{2}{3}\\normalsize x - 2[\/latex] by plotting points or intercepts? Why?<\/p>\n

                            Self Check<\/h2>\n

                            \u24d0 After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.<\/p>\n

                            \"Checklist
                            \n\u24d1 What does this checklist tell you about your mastery of this section? What steps will you take to improve?<\/p>\n

                             <\/p>\n

                            Practice Makes Perfect<\/h2>\n

                            Use Geoboards to Model Slope – CODE THESE in OHM<\/strong>
                            \nIn the following exercises, find the slope modeled on each geoboard.<\/p>\n

                            \"The<\/p>\n

                            [latex]\\Large\\frac{1}{4}[\/latex]<\/p>\n

                            \"The<\/p>\n

                            \"The<\/p>\n

                            [latex]-\\Large\\frac{3}{2}[\/latex]<\/p>\n

                            \"The<\/p>\n

                            In the following exercises, model each slope. Draw a picture to show your results.<\/p>\n

                            [latex]\\Large\\frac{2}{3}[\/latex]<\/p>\n

                            \"The<\/p>\n

                            [latex]\\Large\\frac{3}{4}[\/latex]<\/p>\n

                            [latex]\\Large\\frac{1}{4}[\/latex]<\/p>\n

                            \"The<\/p>\n

                            [latex]\\Large\\frac{4}{3}[\/latex]<\/p>\n

                            [latex]-\\Large\\frac{1}{2}[\/latex]<\/p>\n

                            \"The<\/p>\n

                            [latex]-\\Large\\frac{3}{4}[\/latex]<\/p>\n

                            [latex]-\\Large\\frac{2}{3}[\/latex]<\/p>\n

                            \"The<\/p>\n

                            [latex]-\\Large\\frac{3}{2}[\/latex]<\/p>\n

                            Find the Slope of a Line from its Graph<\/strong>
                            \nIn the following exercises, find the slope of each line shown.<\/p>\n

                            \"The<\/p>\n

                            [latex]\\Large\\frac{2}{5}[\/latex]<\/p>\n

                            \"The<\/p>\n

                            \"The<\/p>\n

                            [latex]\\Large\\frac{5}{4}[\/latex]<\/p>\n

                            \"The<\/p>\n

                            \"The<\/p>\n

                            [latex]-\\Large\\frac{1}{3}[\/latex]<\/p>\n

                            \"The<\/p>\n

                            \"The<\/p>\n

                            [latex]-\\Large\\frac{3}{4}[\/latex]<\/p>\n

                            \"The<\/p>\n

                            \"The<\/p>\n

                            [latex]\\Large\\frac{3}{4}[\/latex]<\/p>\n

                            \"The<\/p>\n

                            \"The<\/p>\n

                            [latex]-\\Large\\frac{5}{2}[\/latex]<\/p>\n

                            \"The<\/p>\n

                            \"The<\/p>\n

                            [latex]-\\Large\\frac{2}{3}[\/latex]<\/p>\n

                            \"The<\/p>\n

                            \"The<\/p>\n

                            [latex]\\Large\\frac{1}{4}[\/latex]<\/p>\n

                            \"The<\/p>\n

                            Find the Slope of Horizontal and Vertical Lines<\/strong>
                            \nIn the following exercises, find the slope of each line.<\/p>\n

                            [latex]y=3[\/latex]<\/p>\n

                            0<\/p>\n

                            [latex]y=1[\/latex]<\/p>\n

                            [latex]x=4[\/latex]<\/p>\n

                            undefined<\/p>\n

                            [latex]x=2[\/latex]<\/p>\n

                            [latex]y=-2[\/latex]<\/p>\n

                            0<\/p>\n

                            [latex]y=-3[\/latex]<\/p>\n

                            [latex]x=-5[\/latex]<\/p>\n

                            undefined<\/p>\n

                            [latex]x=-4[\/latex]<\/p>\n

                            Use the Slope Formula to find the Slope of a Line between Two Points<\/strong>
                            \nIn the following exercises, use the slope formula to find the slope of the line between each pair of points.<\/p>\n

                            [latex]\\left(1,4\\right),\\left(3,9\\right)[\/latex]<\/p>\n

                            [latex]\\Large\\frac{5}{2}[\/latex]<\/p>\n

                            [latex]\\left(2,3\\right),\\left(5,7\\right)[\/latex]<\/p>\n

                            [latex]\\left(0,3\\right),\\left(4,6\\right)[\/latex]<\/p>\n

                            [latex]\\Large\\frac{3}{4}[\/latex]<\/p>\n

                            [latex]\\left(0,1\\right),\\left(5,4\\right)[\/latex]<\/p>\n

                            [latex]\\left(2,5\\right),\\left(4,0\\right)[\/latex]<\/p>\n

                            [latex]-\\Large\\frac{5}{2}[\/latex]<\/p>\n

                            [latex]\\left(3,6\\right),\\left(8,0\\right)[\/latex]<\/p>\n

                            [latex]\\left(-3,3\\right),\\left(2,-5\\right)[\/latex]<\/p>\n

                            [latex]-\\Large\\frac{8}{5}[\/latex]<\/p>\n

                            [latex]\\left(-2,4\\right),\\left(3,-1\\right)[\/latex]<\/p>\n

                            [latex]\\left(-1,-2\\right),\\left(2,5\\right)[\/latex]<\/p>\n

                            [latex]\\Large\\frac{7}{3}[\/latex]<\/p>\n

                            [latex]\\left(-2,-1\\right),\\left(6,5\\right)[\/latex]<\/p>\n

                            [latex]\\left(4,-5\\right),\\left(1,-2\\right)[\/latex]<\/p>\n

                            \u22121<\/p>\n

                            [latex]\\left(3,-6\\right),\\left(2,-2\\right)[\/latex]<\/p>\n

                            Graph a Line Given a Point and the Slope<\/strong>
                            \nIn the following exercises, graph the line given a point and the slope.<\/p>\n

                            [latex]\\left(1,-2\\right);m=\\Large\\frac{3}{4}[\/latex]<\/p>\n

                            \"The<\/p>\n

                            [latex]\\left(1,-1\\right);m=\\Large\\frac{1}{2}[\/latex]<\/p>\n

                            [latex]\\left(2,5\\right);m=-\\Large\\frac{1}{3}[\/latex]<\/p>\n

                            \"The<\/p>\n

                            [latex]\\left(1,4\\right);m=-\\Large\\frac{1}{2}[\/latex]<\/p>\n

                            [latex]\\left(-3,4\\right);m=-\\Large\\frac{3}{2}[\/latex]<\/p>\n

                            \"The<\/p>\n

                            [latex]\\left(-2,5\\right);m=-\\Large\\frac{5}{4}[\/latex]<\/p>\n

                            [latex]\\left(-1,-4\\right);m=\\Large\\frac{4}{3}[\/latex]<\/p>\n

                            \"The<\/p>\n

                            [latex]\\left(-3,-5\\right);m=\\Large\\frac{3}{2}[\/latex]<\/p>\n

                            [latex]\\left(0,3\\right);m=-\\Large\\frac{2}{5}[\/latex]<\/p>\n

                            \"The<\/p>\n

                            [latex]\\left(0,5\\right);m=-\\Large\\frac{4}{3}[\/latex]<\/p>\n

                            [latex]\\left(-2,0\\right);m=\\Large\\frac{3}{4}[\/latex]<\/p>\n

                            \"The<\/p>\n

                            [latex]\\left(-1,0\\right);m=\\Large\\frac{1}{5}[\/latex]<\/p>\n

                            [latex]\\left(-3,3\\right);m=2[\/latex]<\/p>\n

                            \"The<\/p>\n

                            [latex]\\left(-4,2\\right);m=4[\/latex]<\/p>\n

                            [latex]\\left(1,5\\right);m=-3[\/latex]<\/p>\n

                            \"The<\/p>\n

                            [latex]\\left(2,3\\right);m=-1[\/latex]<\/p>\n

                            Solve Slope Applications<\/strong>
                            \nIn the following exercises, solve these slope applications.<\/p>\n

                            Slope of a roof<\/strong> A fairly easy way to determine the slope is to take a [latex]\\text{12-inch}[\/latex] level and set it on one end on the roof surface. Then take a tape measure or ruler, and measure from the other end of the level down to the roof surface. You can use these measurements to calculate the slope of the roof. What is the slope of the roof in this picture?<\/p>\n

                            \"A<\/p>\n

                            [latex]\\Large\\frac{1}{3}[\/latex]<\/p>\n

                            What is the slope of the roof shown?<\/p>\n

                            \"A<\/p>\n

                            Road grade<\/strong> A local road has a grade of [latex]\\text{6%}[\/latex]. The grade of a road is its slope expressed as a percent.<\/p>\n

                              \n
                            1. \u24d0 Find the slope of the road as a fraction and then simplify the fraction.<\/li>\n
                            2. \u24d1 What rise and run would reflect this slope or grade?<\/li>\n<\/ol>\n

                              \u24d0 [latex]\\Large\\frac{3}{50}[\/latex] \u24d1 [latex]\\text{rise}=3;\\text{run}=50[\/latex]<\/p>\n

                              Highway grade<\/strong> A local road rises [latex]2[\/latex] feet for every [latex]50[\/latex] feet of highway.<\/p>\n

                                \n
                              1. \u24d0 What is the slope of the highway?<\/li>\n
                              2. \u24d1 The grade of a highway is its slope expressed as a percent. What is the grade of this highway?<\/li>\n<\/ol>\n

                                Everyday Math<\/h2>\n

                                Wheelchair ramp<\/strong> The rules for wheelchair ramps require a maximum [latex]1[\/latex] inch rise for a [latex]12[\/latex] inch run.<\/p>\n

                                  \n
                                1. \u24d0 How long must the ramp be to accommodate a [latex]\\text{24-inch}[\/latex] rise to the door?<\/li>\n
                                2. \u24d1 Draw a model of this ramp.<\/li>\n<\/ol>\n

                                  \u24d0 288 inches (24 feet)
                                  \n\u24d1 Models will vary.<\/p>\n

                                  Wheelchair ramp<\/strong> A [latex]\\text{1-inch}[\/latex] rise for a [latex]\\text{16-inch}[\/latex] run makes it easier for the wheelchair rider to ascend the ramp.<\/p>\n

                                    \n
                                  1. \u24d0 How long must the ramp be to easily accommodate a [latex]\\text{24-inch}[\/latex] rise to the door?<\/li>\n
                                  2. \u24d1 Draw a model of this ramp.<\/li>\n<\/ol>\n

                                    Writing Exercises<\/h2>\n

                                    What does the sign of the slope tell you about a line?<\/p>\n

                                    Answers will vary.<\/p>\n

                                    How does the graph of a line with slope [latex]m=\\Large\\frac{1}{2}[\/latex] differ from the graph of a line with slope [latex]m=2?[\/latex]<\/p>\n

                                    Why is the slope of a vertical line undefined?<\/p>\n

                                    Answers will vary.<\/p>\n

                                    Explain how you can graph a line given a point and its slope.<\/p>\n

                                    Self Check<\/h2>\n

                                    \u24d0 After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.<\/p>\n

                                    \"Checklist
                                    \n\u24d1 On a scale of 1\u201310, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?<\/p>\n

                                    Chapter Review Exercises<\/h1>\n

                                    Use the Rectangular Coordinate System<\/h2>\n

                                    Plot Points in a Rectangular Coordinate System<\/strong>
                                    \nIn the following exercises, plot each point in a rectangular coordinate system.<\/p>\n

                                    [latex]\\left(1,3\\right),\\left(3,1\\right)[\/latex]<\/p>\n

                                    \"The<\/p>\n

                                    [latex]\\left(2,5\\right),\\left(5,2\\right)[\/latex]<\/p>\n

                                    In the following exercises, plot each point in a rectangular coordinate system and identify the quadrant in which the point is located.<\/p>\n

                                      \n
                                    1. \u24d0 [latex]\\left(-1,-5\\right)[\/latex]<\/li>\n
                                    2. \u24d1 [latex]\\left(-3,4\\right)[\/latex]<\/li>\n
                                    3. \u24d2 [latex]\\left(2,-3\\right)[\/latex]<\/li>\n
                                    4. \u24d3 [latex]\\left(1,\\Large\\frac{5}{2}\\normalsize\\right)[\/latex]<\/li>\n<\/ol>\n

                                      \u24d0 III
                                      \n\u24d1 II
                                      \n\u24d2 IV
                                      \n\u24d0 I<\/p>\n

                                        \n
                                      1. \u24d0 [latex]\\left(3,-2\\right)[\/latex]<\/li>\n
                                      2. \u24d1 [latex]\\left(-4,-1\\right)[\/latex]<\/li>\n
                                      3. \u24d2 [latex]\\left(-5,4\\right)[\/latex]<\/li>\n
                                      4. \u24d3 [latex]\\left(2,\\Large\\frac{10}{3}\\normalsize\\right)[\/latex]<\/li>\n<\/ol>\n

                                        Identify Points on a Graph<\/strong>
                                        \nIn the following exercises, name the ordered pair of each point shown in the rectangular coordinate system.<\/p>\n

                                        \"The<\/p>\n

                                        \u24d0 (5,3)
                                        \n\u24d1 (2,\u22121)
                                        \n\u24d2 (\u22123,\u22122)
                                        \n\u24d3 (\u22121,4)<\/p>\n

                                        \"The<\/p>\n

                                        \"The<\/p>\n

                                        \u24d0 (2,0)
                                        \n\u24d1 (0,\u22125)
                                        \n\u24d2 (\u22124,0)
                                        \n\u24d3 (0,3)<\/p>\n

                                        \"The<\/p>\n

                                        Verify Solutions to an Equation in Two Variables<\/strong>
                                        \nIn the following exercises, find the ordered pairs that are solutions to the given equation.<\/p>\n

                                        [latex]5x+y=10[\/latex]<\/p>\n

                                          \n
                                        1. \u24d0 [latex]\\left(5,1\\right)[\/latex]<\/li>\n
                                        2. \u24d1 [latex]\\left(2,0\\right)[\/latex]<\/li>\n
                                        3. \u24d2 [latex]\\left(4,-10\\right)[\/latex]<\/li>\n<\/ol>\n

                                          \u24d1,\u24d2<\/p>\n

                                          [latex]y=6x - 2[\/latex]<\/p>\n

                                            \n
                                          1. \u24d0 [latex]\\left(1,4\\right)[\/latex]<\/li>\n
                                          2. \u24d1 [latex]\\left(\\Large\\frac{1}{3}\\normalsize ,0\\right)[\/latex]<\/li>\n
                                          3. \u24d2 [latex]\\left(6,-2\\right)[\/latex]<\/li>\n<\/ol>\n

                                            Complete a Table of Solutions to a Linear Equation in Two Variables<\/strong>
                                            \nIn the following exercises, complete the table to find solutions to each linear equation.<\/p>\n

                                            [latex]y=4x - 1[\/latex]<\/p>\n\n\n\n\n\n\n\n
                                            [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n[latex]\\left(x,y\\right)[\/latex]<\/th>\n<\/tr>\n<\/thead>\n
                                            [latex]0[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
                                            [latex]1[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
                                            [latex]-2[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n\n\n
                                            [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n[latex]\\left(x,y\\right)[\/latex]<\/th>\n<\/tr>\n<\/thead>\n
                                            [latex]0[\/latex]<\/td>\n[latex]-1[\/latex]<\/td>\n[latex]\\left(0,-1\\right)[\/latex]<\/td>\n<\/tr>\n
                                            [latex]1[\/latex]<\/td>\n[latex]3[\/latex]<\/td>\n[latex]\\left(1,3\\right)[\/latex]<\/td>\n<\/tr>\n
                                            [latex]-2[\/latex]<\/td>\n[latex]-9[\/latex]<\/td>\n[latex]\\left(-2,-9\\right)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                                            [latex]y=-\\Large\\frac{1}{2}\\normalsize x+3[\/latex]<\/p>\n\n\n\n\n\n\n\n
                                            [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n[latex]\\left(x,y\\right)[\/latex]<\/th>\n<\/tr>\n<\/thead>\n
                                            [latex]0[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
                                            [latex]1[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
                                            [latex]-2[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                                            [latex]x+2y=5[\/latex]<\/p>\n\n\n\n\n\n\n\n
                                            [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n[latex]\\left(x,y\\right)[\/latex]<\/th>\n<\/tr>\n<\/thead>\n
                                            <\/td>\n[latex]0[\/latex]<\/td>\n<\/td>\n<\/tr>\n
                                            [latex]1[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
                                            [latex]-1[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n\n\n
                                            [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n[latex]\\left(x,y\\right)[\/latex]<\/th>\n<\/tr>\n<\/thead>\n
                                            [latex]5[\/latex]<\/td>\n[latex]0[\/latex]<\/td>\n[latex]\\left(5,0\\right)[\/latex]<\/td>\n<\/tr>\n
                                            [latex]1[\/latex]<\/td>\n[latex]2[\/latex]<\/td>\n[latex]\\left(1,2\\right)[\/latex]<\/td>\n<\/tr>\n
                                            [latex]-1[\/latex]<\/td>\n[latex]3[\/latex]<\/td>\n[latex]\\left(-1,3\\right)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                                            [latex]3x - 2y=6[\/latex]<\/p>\n\n\n\n\n\n\n\n
                                            [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n[latex]\\left(x,y\\right)[\/latex]<\/th>\n<\/tr>\n<\/thead>\n
                                            [latex]0[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
                                            <\/td>\n[latex]0[\/latex]<\/td>\n<\/td>\n<\/tr>\n
                                            [latex]-2[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                                            Find Solutions to a Linear Equation in Two Variables<\/strong>
                                            \nIn the following exercises, find three solutions to each linear equation.<\/p>\n

                                            [latex]x+y=3[\/latex]<\/p>\n

                                            Answers will vary.<\/p>\n

                                            [latex]x+y=-4[\/latex]<\/p>\n

                                            [latex]y=3x+1[\/latex]<\/p>\n

                                            Answers will vary.<\/p>\n

                                            [latex]y=-x - 1[\/latex]<\/p>\n

                                            Graphing Linear Equations<\/h2>\n

                                            Recognize the Relation Between the Solutions of an Equation and its Graph<\/strong>
                                            \nIn the following exercises, for each ordered pair, decide<\/p>\n

                                            \u24d0 if the ordered pair is a solution to the equation.
                                            \n\u24d1 if the point is on the line.<\/p>\n

                                            [latex]y=-x+4[\/latex]<\/p>\n

                                              \n
                                            1. \u24d0 [latex]\\left(0,4\\right)[\/latex]<\/li>\n
                                            2. \u24d1 [latex]\\left(-1,3\\right)[\/latex]<\/li>\n
                                            3. \u24d2 [latex]\\left(2,2\\right)[\/latex]<\/li>\n
                                            4. \u24d3 [latex]\\left(-2,6\\right)[\/latex]<\/li>\n<\/ol>\n

                                              \"The<\/p>\n

                                              \u24d0 yes \u24d1 no \u24d2 yes \u24d3 yes
                                              \n\u24d0 yes \u24d1 no \u24d2 yes \u24d3 yes<\/p>\n

                                              [latex]y=\\Large\\frac{2}{3}\\normalsize x - 1[\/latex]<\/p>\n

                                                \n
                                              1. \u24d0 [latex]\\left(0,-1\\right)[\/latex]<\/li>\n
                                              2. \u24d1 [latex]\\left(3,1\\right)[\/latex]<\/li>\n
                                              3. \u24d2 [latex]\\left(-3,-3\\right)[\/latex]<\/li>\n
                                              4. \u24d3 [latex]\\left(6,4\\right)[\/latex]<\/li>\n<\/ol>\n

                                                \"The<\/p>\n

                                                Graph a Linear Equation by Plotting Points<\/strong>
                                                \nIn the following exercises, graph by plotting points.<\/p>\n

                                                [latex]y=4x - 3[\/latex]<\/p>\n

                                                \"The<\/p>\n

                                                [latex]y=-3x[\/latex]<\/p>\n

                                                [latex]2x+y=7[\/latex]<\/p>\n

                                                \"The<\/p>\n

                                                Graph Vertical and Horizontal lines<\/strong>
                                                \nIn the following exercises, graph the vertical or horizontal lines.<\/p>\n

                                                [latex]y=-2[\/latex]<\/p>\n

                                                [latex]x=3[\/latex]<\/p>\n

                                                \"The<\/p>\n

                                                Graphing with Intercepts<\/h2>\n

                                                Identify the Intercepts on a Graph<\/strong>
                                                \nIn the following exercises, find the [latex]x\\text{-}[\/latex] and [latex]y\\text{-intercepts}[\/latex].<\/p>\n

                                                \"The<\/p>\n

                                                \"The<\/p>\n

                                                (0,3) (3,0)<\/p>\n

                                                Find the Intercepts from an Equation of a Line<\/strong>
                                                \nIn the following exercises, find the intercepts.<\/p>\n

                                                [latex]x+y=5[\/latex]<\/p>\n

                                                [latex]x-y=-1[\/latex]<\/p>\n

                                                (\u22121,0) (0,1)<\/p>\n

                                                [latex]y=\\Large\\frac{3}{4}\\normalsize x - 12[\/latex]<\/p>\n

                                                [latex]y=3x[\/latex]<\/p>\n

                                                (0,0)<\/p>\n

                                                Graph a Line Using the Intercepts<\/strong>
                                                \nIn the following exercises, graph using the intercepts.<\/p>\n

                                                [latex]-x+3y=3[\/latex]<\/p>\n

                                                [latex]x+y=-2[\/latex]<\/p>\n

                                                \"This<\/p>\n

                                                Choose the Most Convenient Method to Graph a Line<\/strong>
                                                \nIn the following exercises, identify the most convenient method to graph each line.<\/p>\n

                                                [latex]x=5[\/latex]<\/p>\n

                                                [latex]y=-3[\/latex]<\/p>\n

                                                horizontal line<\/p>\n

                                                [latex]2x+y=5[\/latex]<\/p>\n

                                                [latex]x-y=2[\/latex]<\/p>\n

                                                intercepts<\/p>\n

                                                [latex]y=\\Large\\frac{1}{2}\\normalsize x+2[\/latex]<\/p>\n

                                                [latex]y=\\Large\\frac{3}{4}\\normalsize x - 1[\/latex]<\/p>\n

                                                plotting points<\/p>\n

                                                Understand Slope of a Line<\/h2>\n

                                                Use Geoboards to Model Slope<\/strong>
                                                \nIn the following exercises, find the slope modeled on each geoboard.<\/p>\n

                                                \"The<\/p>\n

                                                \"The<\/p>\n

                                                [latex]\\Large\\frac{4}{3}[\/latex]<\/p>\n

                                                \"The<\/p>\n

                                                \"The<\/p>\n

                                                [latex]-\\Large\\frac{2}{3}[\/latex]<\/p>\n

                                                In the following exercises, model each slope. Draw a picture to show your results.<\/p>\n

                                                [latex]\\Large\\frac{1}{3}[\/latex]<\/p>\n

                                                [latex]\\Large\\frac{3}{2}[\/latex]<\/p>\n

                                                \"The<\/p>\n

                                                [latex]-\\Large\\frac{2}{3}[\/latex]<\/p>\n

                                                [latex]-\\Large\\frac{1}{2}[\/latex]<\/p>\n

                                                \"The<\/p>\n

                                                Find the Slope of a Line from its Graph<\/strong>
                                                \nIn the following exercises, find the slope of each line shown.<\/p>\n

                                                \"The<\/p>\n

                                                \"The<\/p>\n

                                                1<\/p>\n

                                                \"The<\/p>\n

                                                \"The<\/p>\n

                                                [latex]-\\Large\\frac{1}{2}[\/latex]<\/p>\n

                                                Find the Slope of Horizontal and Vertical Lines<\/strong>
                                                \nIn the following exercises, find the slope of each line.<\/p>\n

                                                [latex]y=2[\/latex]<\/p>\n

                                                [latex]x=5[\/latex]<\/p>\n

                                                undefined<\/p>\n

                                                [latex]x=-3[\/latex]<\/p>\n

                                                [latex]y=-1[\/latex]<\/p>\n

                                                0<\/p>\n

                                                Use the Slope Formula to find the Slope of a Line between Two Points<\/strong>
                                                \nIn the following exercises, use the slope formula to find the slope of the line between each pair of points.<\/p>\n

                                                [latex]\\left(2,1\\right),\\left(4,5\\right)[\/latex]<\/p>\n

                                                [latex]\\left(-1,-1\\right),\\left(0,-5\\right)[\/latex]<\/p>\n

                                                \u22124<\/p>\n

                                                [latex]\\left(3,5\\right),\\left(4,-1\\right)[\/latex]<\/p>\n

                                                [latex]\\left(-5,-2\\right),\\left(3,2\\right)[\/latex]<\/p>\n

                                                [latex]\\Large\\frac{1}{2}[\/latex]<\/p>\n

                                                Graph a Line Given a Point and the Slope<\/strong>
                                                \nIn the following exercises, graph the line given a point and the slope.<\/p>\n

                                                [latex]\\left(2,-2\\right);m=\\Large\\frac{5}{2}[\/latex]<\/p>\n

                                                [latex]\\left(-3,4\\right);m=-\\Large\\frac{1}{3}[\/latex]<\/p>\n

                                                \"The<\/p>\n

                                                Solve Slope Applications<\/strong>
                                                \nIn the following exercise, solve the slope application.<\/p>\n

                                                A roof has rise [latex]10[\/latex] feet and run [latex]15[\/latex] feet. What is its slope?<\/p>\n

                                                Chapter Practice Test<\/h1>\n

                                                Plot and label these points:<\/p>\n

                                                  \n
                                                1. \u24d0 [latex]\\left(2,5\\right)[\/latex]<\/li>\n
                                                2. \u24d1 [latex]\\left(-1,-3\\right)[\/latex]<\/li>\n
                                                3. \u24d2 [latex]\\left(-4,0\\right)[\/latex]<\/li>\n
                                                4. \u24d3 [latex]\\left(3,-5\\right)[\/latex]<\/li>\n
                                                5. \u24d4 [latex]\\left(-2,1\\right)[\/latex]<\/li>\n<\/ol>\n

                                                  \"The<\/p>\n

                                                  Name the ordered pair for each point shown.<\/p>\n

                                                  \"The<\/p>\n

                                                  Find the [latex]x\\text{-intercept}[\/latex] and [latex]y\\text{-intercept}[\/latex] on the line shown.<\/p>\n

                                                  \"The<\/p>\n

                                                  (4,0), (0,\u22122)<\/p>\n

                                                  Find the [latex]x\\text{-intercept}[\/latex] and [latex]y\\text{-intercept}[\/latex] of the equation [latex]3x-y=6[\/latex].<\/p>\n

                                                  Is [latex]\\left(1,3\\right)[\/latex] a solution to the equation [latex]x+4y=12?[\/latex] How do you know?<\/p>\n

                                                  no; 1 + 4 \u00b7 3 \u2260 12<\/p>\n

                                                  Complete the table to find four solutions to the equation [latex]y=-x+1[\/latex].<\/p>\n\n\n\n\n\n\n\n
                                                  [latex]x[\/latex]<\/td>\n[latex]y[\/latex]<\/td>\n[latex]\\left(x,y\\right)[\/latex]<\/td>\n<\/tr>\n
                                                  [latex]0[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
                                                  [latex]1[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
                                                  [latex]3[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
                                                  [latex]-2[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                                                  Complete the table to find three solutions to the equation [latex]4x+y=8[\/latex]<\/p>\n\n\n\n\n\n\n
                                                  [latex]x[\/latex]<\/td>\n[latex]y[\/latex]<\/td>\n[latex]\\left(x,y\\right)[\/latex]<\/td>\n<\/tr>\n
                                                  [latex]0[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
                                                  <\/td>\n[latex]0[\/latex]<\/td>\n<\/td>\n<\/tr>\n
                                                  [latex]3[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n\n
                                                  [latex]x[\/latex]<\/td>\n[latex]y[\/latex]<\/td>\n[latex]\\left(x,y\\right)[\/latex]<\/td>\n<\/tr>\n
                                                  [latex]0[\/latex]<\/td>\n[latex]8[\/latex]<\/td>\n[latex]\\left(0,8\\right)[\/latex]<\/td>\n<\/tr>\n
                                                  [latex]2[\/latex]<\/td>\n[latex]0[\/latex]<\/td>\n[latex]\\left(2,0\\right)[\/latex]<\/td>\n<\/tr>\n
                                                  [latex]3[\/latex]<\/td>\n[latex]-4[\/latex]<\/td>\n[latex]\\left(3,-4\\right)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                                                  In the following exercises, find three solutions to each equation and then graph each line.<\/p>\n

                                                  [latex]y=-3x[\/latex]<\/p>\n

                                                  [latex]2x+3y=-6[\/latex]<\/p>\n

                                                  \"The<\/p>\n

                                                  In the following exercises, find the slope of each line.<\/p>\n

                                                  \"The<\/p>\n

                                                  \"The<\/p>\n

                                                  [latex]-\\Large\\frac{5}{2}[\/latex]<\/p>\n

                                                  Use the slope formula to find the slope of the line between [latex]\\left(0,-4\\right)[\/latex] and [latex]\\left(5,2\\right)[\/latex].<\/p>\n

                                                  Find the slope of the line [latex]y=2[\/latex].<\/p>\n

                                                  0<\/p>\n

                                                  Graph the line passing through [latex]\\left(1,1\\right)[\/latex] with slope [latex]m=\\Large\\frac{3}{2}[\/latex].<\/p>\n

                                                  A bicycle route climbs [latex]20[\/latex] feet for [latex]1,000[\/latex] feet of horizontal distance. What is the slope of the route?<\/p>\n

                                                  [latex]\\Large\\frac{1}{50}[\/latex]<\/p>\n\n\t\t\t

                                                  \n\t\t\t

                                                  Candela Citations<\/h3>\n\t\t\t\t\t
                                                  \n\t\t\t\t\t\t
                                                  \n\t\t\t\t\t\t\t
                                                  CC licensed content, Specific attribution<\/div>